From e2051c5a41596dfc45f8ab9c92af5b442e0fe18a Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 14:38:36 +0200
Subject: [PATCH 01/21] cultmath map: Pass 9c root cause of the
 span_fbm/span_ridged 1-ulp diff (entry -O3 reassociation, lavapipe use-count
 fusion); strict-form probes

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 docs/cultmath-interval-ground-cut.md          | 29 ++++++++++
 .../native-shader-probes/strict-form/nc.py    | 11 ++++
 .../strict-form/probe1.sh                     | 19 +++++++
 .../strict-form/probe2.sh                     | 46 ++++++++++++++++
 .../strict-form/probe3.sh                     | 53 +++++++++++++++++++
 .../strict-form/probe4.sh                     | 53 +++++++++++++++++++
 6 files changed, 211 insertions(+)
 create mode 100644 docs/research/native-shader-probes/strict-form/nc.py
 create mode 100644 docs/research/native-shader-probes/strict-form/probe1.sh
 create mode 100644 docs/research/native-shader-probes/strict-form/probe2.sh
 create mode 100644 docs/research/native-shader-probes/strict-form/probe3.sh
 create mode 100644 docs/research/native-shader-probes/strict-form/probe4.sh

diff --git a/docs/cultmath-interval-ground-cut.md b/docs/cultmath-interval-ground-cut.md
index 2cce2d75..8e86b70e 100644
--- a/docs/cultmath-interval-ground-cut.md
+++ b/docs/cultmath-interval-ground-cut.md
@@ -2340,6 +2340,35 @@ and 16:50 UTC (18:30 to 18:50 CEST). Logs are in the Imagination scratchpad
     the committed GLSL is 80, 9, 10, 18. `--relax-nan-checks` changes no lavapipe bit. So the
     cleaned route is closer to the HLSL than today's GLSL is, and "bit-identical to today's
     lowering" cannot be its gate. With apt's spirv-tools 2025.1~rc1 the figures for this route are the same.
+- **Why `span_fbm` and `span_ridged` differ by 1 ulp (Pass 9c).** Imagination `imagination-ag4-span-ulp`,
+  2026-10-17, on 23ac4e89, same image and tools as `cut-glsl-build-dxc.h1`, probes in the session
+  scratchpad `logs/ag4-ulp/` (`probe1.sh` to `probe4.sh`). Only the curvature word (word 4 of 6) differs, in
+  41 and 42 of 1536 words. Two causes, both measured:
+  - **dxc's entry-point optimiser reassociates.** `cultmath_snoise_hessian` ends every entry in
+    `105.0 * (...)`. In the `-O3` entry module the 105 is hoisted out: nine squares are summed bare and
+    the sum is multiplied once (`OpFMul %11025 %sum`, then `Sqrt`), where the source squares `105 * a`
+    nine times. That is real arithmetic, not float arithmetic. Neither `NoContraction` nor
+    `--relax-nan-checks` touches it. `dxc -Gis` (IEEE strictness) stops it.
+  - **The driver contracts mul+add by use count.** lavapipe (NIR) fuses an `OpFMul` into the `OpFAdd`
+    that consumes it only when the product has one use. dxc's CSE shares the symmetric Hessian's
+    off-diagonal squares (two uses each), so the entry module fuses some of the nine pairs; the `-Od`
+    library module has nine single-use products and fuses all nine. The `OpFAdd` order is the same in
+    both (left fold, as the C# `span_frobenius`).
+  - Decorating every `OpFMul`, `OpFAdd`, `OpFSub`, `OpVectorTimesScalar` and `OpDot` `NoContraction` in
+    both final modules, f103 and f104: `-Od` HLSL equals the built GLSL (0 words differ); `-O3`
+    HLSL still differs in 31 and 44 (the hoist). `-Gis` (with `-O3`) plus `NoContraction` equals the built GLSL on
+    127 of 127 families, and so does `-Od` plus `NoContraction`. Plain `-Od` HLSL differs from the built GLSL in 664 words
+    (contraction depends on use structure), so `-Od` alone is worse than `-O3`: your suspicion of `-Od`
+    on the HLSL route is not a fix.
+  - **Which is right.** Against the C# fixture, exact cases of 256 for f103 are 3 (HLSL) and 4 (GLSL) plain,
+    and 151 for both under `NoContraction`; for f104, 7 and 10 plain, 141 under it. Of the first 60 families whose
+    count moved, the strict form is nearer the C# in all but one, which moved by 1. Strict IEEE, no contraction, no
+    reassociation is what C# computes, so it is "right"; the plain routes are each one driver's
+    fusion pattern. The built GLSL is source-faithful (nothing in the `-Od` route reassociates).
+  - **What makes them agree.** The equality gate (`GLSL_DIR` mode) compares both routes in the strict
+    form: HLSL entry built with `-Gis`, and a harness pass that adds `NoContraction` to every float op of
+    both modules (about 12 lines of `spirv-dis` and `spirv-as`; `tools/device/nc.py` in the probe). That is
+    127 of 127. The shipped GLSL and the C# bounds judge are unchanged. See question `glsl-gate-strict-form`.
 - **Capability strip.** `spirv-opt --trim-capabilities` (spirv-tools 2025.1~rc1) leaves all 14
   capabilities and both extensions in place, and SPIRV-Cross still refuses ("RayQuery requires Vulkan
   GLSL 460"). Stripping every capability except Shader and Linkage and every OpExtension in the
diff --git a/docs/research/native-shader-probes/strict-form/nc.py b/docs/research/native-shader-probes/strict-form/nc.py
new file mode 100644
index 00000000..4771b66c
--- /dev/null
+++ b/docs/research/native-shader-probes/strict-form/nc.py
@@ -0,0 +1,11 @@
+import re,sys
+src,dst=sys.argv[1:3]
+L=open(src).read().split('\n')
+ids=[]
+for l in L:
+    m=re.match(r'\s*(%\w+) = Op(FMul|FAdd|FSub|VectorTimesScalar|Dot)\b',l)
+    if m: ids.append(m.group(1))
+i=next(k for k,l in enumerate(L) if re.search(r'= OpType',l))
+L[i:i]=['               OpDecorate %s NoContraction'%x for x in ids]
+open(dst,'w').write('\n'.join(L))
+print(src,len(ids))
diff --git a/docs/research/native-shader-probes/strict-form/probe1.sh b/docs/research/native-shader-probes/strict-form/probe1.sh
new file mode 100644
index 00000000..f0baa154
--- /dev/null
+++ b/docs/research/native-shader-probes/strict-form/probe1.sh
@@ -0,0 +1,19 @@
+set -e
+apt-get update -qq >/dev/null; apt-get install -y -qq --no-install-recommends python3 spirv-tools >/dev/null 2>&1
+P=packages/cultmath/tools
+python3 - <<'PY'
+p='packages/cultmath/tools/device/run-lavapipe.sh'
+s=open(p).read()
+k='python3 "$DEV/gen.py" "$W/work" "$CM"\n'
+s=s.replace(k,k+'sed -i -E "s/[.](cos|sin)([^A-Za-z0-9_])/._\1\2/g" "$W"/work/*.comp\ngrep -E "^f10[34]\t" "$W/work/manifest.txt" >"$W/work/m2"; mv "$W/work/m2" "$W/work/manifest.txt"\n')
+open(p,'w').write(s)
+PY
+bash $P/glsl/build-glsl.sh /tmp/glslout >/dev/null
+GLSL_DIR=/tmp/glslout bash $P/device/run-lavapipe.sh 2>&1 | tail -4 || true
+W=/tmp/device/work
+for t in f103 f104; do for r in h g; do
+  spirv-dis --raw-id $W/$t.$r.spv -o /tmp/$t.$r.dis
+  echo "== $t $r: NoContraction $(grep -c NoContraction /tmp/$t.$r.dis) Fma $(grep -c ' Fma ' /tmp/$t.$r.dis) FMul $(grep -c OpFMul /tmp/$t.$r.dis) FAdd $(grep -c OpFAdd /tmp/$t.$r.dis) FSub $(grep -c OpFSub /tmp/$t.$r.dis) lines $(wc -l </tmp/$t.$r.dis)"
+done; done
+mkdir -p /tmp/dump; cp /tmp/f10?.?.dis /tmp/dump/; cp $W/f103.hlsl $W/f103.comp /tmp/dump/; cp /tmp/glslout/*.glsl /tmp/dump/
+echo DUMP-BEGIN; tar czf - -C /tmp dump | base64 -w0; echo; echo DUMP-END
diff --git a/docs/research/native-shader-probes/strict-form/probe2.sh b/docs/research/native-shader-probes/strict-form/probe2.sh
new file mode 100644
index 00000000..70cab72e
--- /dev/null
+++ b/docs/research/native-shader-probes/strict-form/probe2.sh
@@ -0,0 +1,46 @@
+set -e
+apt-get update -qq >/dev/null; apt-get install -y -qq --no-install-recommends python3 spirv-tools >/dev/null 2>&1
+cat >/tmp/nc.py <<'PYEOF'
+import re,sys
+src,dst=sys.argv[1:3]
+L=open(src).read().split('\n')
+ids=[]
+for l in L:
+    m=re.match(r'\s*(%\w+) = Op(FMul|FAdd|FSub|VectorTimesScalar|Dot)\b',l)
+    if m: ids.append(m.group(1))
+i=next(k for k,l in enumerate(L) if re.search(r'= OpType',l))
+L[i:i]=['               OpDecorate %s NoContraction'%x for x in ids]
+open(dst,'w').write('\n'.join(L))
+print(src,len(ids))
+PYEOF
+P=packages/cultmath/tools
+python3 - <<'PY'
+p='packages/cultmath/tools/device/run-lavapipe.sh'
+s=open(p).read()
+k='python3 "$DEV/gen.py" "$W/work" "$CM"\n'
+s=s.replace(k,k+'sed -i -E "s/[.](cos|sin)([^A-Za-z0-9_])/._\1\2/g" "$W"/work/*.comp\ngrep -E "^f10[34]\t" "$W/work/manifest.txt" >"$W/work/m2"; mv "$W/work/m2" "$W/work/manifest.txt"\n')
+open(p,'w').write(s)
+PY
+bash $P/glsl/build-glsl.sh /tmp/glslout >/dev/null
+GLSL_DIR=/tmp/glslout bash $P/device/run-lavapipe.sh 2>&1 | tail -4 || true
+W=/tmp/device/work; R=/tmp/device
+mkdir -p $R/nc/lavapipe-hlsl $R/nc/lavapipe-glsl
+while IFS=$'\t' read -r tag _ _ n _ wout; do
+ for r in h g; do
+  spirv-dis --raw-id $W/$tag.$r.spv -o /tmp/$tag.$r.dis
+  python3 /tmp/nc.py /tmp/$tag.$r.dis /tmp/$tag.$r.nc.dis
+  spirv-as --target-env vulkan1.2 /tmp/$tag.$r.nc.dis -o $W/$tag.$r.nc.spv
+  spirv-val --target-env vulkan1.2 $W/$tag.$r.nc.spv
+  d=hlsl; [ $r = g ] && d=glsl
+  $R/vkrun $W/$tag.$r.nc.spv $W/$tag.in $R/nc/lavapipe-$d/$tag.out $n $wout >/dev/null
+ done
+ echo "$tag nc: hlsl==glsl $(cmp -s $R/nc/lavapipe-hlsl/$tag.out $R/nc/lavapipe-glsl/$tag.out && echo YES || echo NO); nc-hlsl==plain-hlsl $(cmp -s $R/nc/lavapipe-hlsl/$tag.out $R/results/lavapipe-hlsl/$tag.out && echo YES || echo NO); nc-glsl==plain-glsl $(cmp -s $R/nc/lavapipe-glsl/$tag.out $R/results/lavapipe-glsl/$tag.out && echo YES || echo NO)"
+done <$W/manifest.txt
+cp /tmp/device/vkrun /tmp/ 2>/dev/null || true
+export CULTMATH_DEVICE_NAME=$(sort -u $R/device.txt | head -1 | sed 's/^device=//') CULTMATH_DEVICE_IDENTITY=x CULTMATH_WRITE_DEVICE_BOUNDS=1
+for v in results nc; do
+  export CULTMATH_DEVICE_RESULTS=$R/$v
+  dotnet test packages/cultmath/tests/CultMath.Tests --no-build --filter "FullyQualifiedName~GlslMirrorTests.DeviceResultsHoldFixture" >/tmp/judge.$v.log 2>&1 || true
+  echo "== judge $v"; grep -E "^(lavapipe-)" packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt | grep -E "	10[34]	" | cut -f1,2,5,6 || tail -5 /tmp/judge.$v.log
+  tail -3 /tmp/judge.$v.log
+done
diff --git a/docs/research/native-shader-probes/strict-form/probe3.sh b/docs/research/native-shader-probes/strict-form/probe3.sh
new file mode 100644
index 00000000..d1585a9e
--- /dev/null
+++ b/docs/research/native-shader-probes/strict-form/probe3.sh
@@ -0,0 +1,53 @@
+set -e
+apt-get update -qq >/dev/null; apt-get install -y -qq --no-install-recommends python3 spirv-tools >/dev/null 2>&1
+cat >/tmp/nc.py <<'PYEOF'
+import re,sys
+src,dst=sys.argv[1:3]
+L=open(src).read().split('\n')
+ids=[]
+for l in L:
+    m=re.match(r'\s*(%\w+) = Op(FMul|FAdd|FSub|VectorTimesScalar|Dot)\b',l)
+    if m: ids.append(m.group(1))
+i=next(k for k,l in enumerate(L) if re.search(r'= OpType',l))
+L[i:i]=['               OpDecorate %s NoContraction'%x for x in ids]
+open(dst,'w').write('\n'.join(L))
+print(src,len(ids))
+PYEOF
+P=packages/cultmath/tools
+python3 - <<'PY'
+p='packages/cultmath/tools/device/run-lavapipe.sh'
+s=open(p).read()
+k='python3 "$DEV/gen.py" "$W/work" "$CM"\n'
+s=s.replace(k,k+'sed -i -E "s/[.](cos|sin)([^A-Za-z0-9_])/._\1\2/g" "$W"/work/*.comp\ngrep -E "^f10[34]\t" "$W/work/manifest.txt" >"$W/work/m2"; mv "$W/work/m2" "$W/work/manifest.txt"\n')
+open(p,'w').write(s)
+PY
+bash $P/glsl/build-glsl.sh /tmp/glslout >/dev/null
+GLSL_DIR=/tmp/glslout bash $P/device/run-lavapipe.sh 2>&1 | tail -4 || true
+W=/tmp/device/work; R=/tmp/device
+DXC=$(find $R/dxc -name dxc -type f | head -1); export LD_LIBRARY_PATH=$(dirname $DXC)/../lib:$(dirname $DXC)
+CM=packages/cultmath
+cat >/tmp/cnt.py <<'PYEOF'
+import sys,struct
+a=open(sys.argv[1],'rb').read();b=open(sys.argv[2],'rb').read()
+n=len(a)//4;x=struct.unpack('<%dI'%n,a);y=struct.unpack('<%dI'%n,b)
+d=[i for i in range(n) if x[i]!=y[i]]
+print(len(d),'of',n,'cols',sorted(set(i%6 for i in d)))
+PYEOF
+run() { # name spv tag n wout
+  $R/vkrun $2 $W/$3.in /tmp/o.$1.$3 $4 $5 >/dev/null; }
+OPT="--target-env=spv1.5 --eliminate-local-single-store --eliminate-dead-code-aggressive"
+while IFS=$'	' read -r tag _ _ n _ wout; do
+ for r in h g; do spirv-dis --raw-id $W/$tag.$r.spv -o /tmp/$tag.$r.dis; python3 /tmp/nc.py /tmp/$tag.$r.dis /tmp/$tag.$r.nc.dis >/dev/null; spirv-as --target-env vulkan1.2 /tmp/$tag.$r.nc.dis -o $W/$tag.$r.nc.spv; done
+ # h variants
+ $DXC -T cs_6_0 -E main -HV 2021 -spirv -fspv-target-env=vulkan1.2 -Od -I $CM/shaders $W/$tag.hlsl -Fo $W/$tag.hOd.spv >/dev/null 2>&1
+ spirv-opt $OPT $W/$tag.hOd.spv -o $W/$tag.hOdO.spv
+ for v in hOd hOdO; do spirv-dis --raw-id $W/$tag.$v.spv -o /tmp/$tag.$v.dis; python3 /tmp/nc.py /tmp/$tag.$v.dis /tmp/$tag.$v.nc.dis >/dev/null; spirv-as --target-env vulkan1.2 /tmp/$tag.$v.nc.dis -o $W/$tag.$v.nc.spv; done
+ for v in h g hOd hOdO; do run $v $W/$tag.$v.spv $tag $n $wout; run $v.nc $W/$tag.$v.nc.spv $tag $n $wout; done
+ for v in h hOd hOdO; do
+  echo "$tag $v vs g: $(python3 /tmp/cnt.py /tmp/o.$v.$tag /tmp/o.g.$tag)"
+  echo "$tag $v.nc vs g.nc: $(python3 /tmp/cnt.py /tmp/o.$v.nc.$tag /tmp/o.g.nc.$tag)"
+ done
+ echo "$tag h.nc vs h: $(python3 /tmp/cnt.py /tmp/o.h.nc.$tag /tmp/o.h.$tag)"
+ echo "$tag g.nc vs g: $(python3 /tmp/cnt.py /tmp/o.g.nc.$tag /tmp/o.g.$tag)"
+ echo "$tag hOd.nc vs hOd: $(python3 /tmp/cnt.py /tmp/o.hOd.nc.$tag /tmp/o.hOd.$tag)"
+done <$W/manifest.txt
diff --git a/docs/research/native-shader-probes/strict-form/probe4.sh b/docs/research/native-shader-probes/strict-form/probe4.sh
new file mode 100644
index 00000000..5b521cf9
--- /dev/null
+++ b/docs/research/native-shader-probes/strict-form/probe4.sh
@@ -0,0 +1,53 @@
+set -e
+apt-get update -qq >/dev/null; apt-get install -y -qq --no-install-recommends python3 spirv-tools >/dev/null 2>&1
+cat >/tmp/nc.py <<'PYEOF'
+import re,sys
+src,dst=sys.argv[1:3]
+L=open(src).read().split('\n')
+ids=[]
+for l in L:
+    m=re.match(r'\s*(%\w+) = Op(FMul|FAdd|FSub|VectorTimesScalar|Dot)\b',l)
+    if m: ids.append(m.group(1))
+i=next(k for k,l in enumerate(L) if re.search(r'= OpType',l))
+L[i:i]=['               OpDecorate %s NoContraction'%x for x in ids]
+open(dst,'w').write('\n'.join(L))
+print(src,len(ids))
+PYEOF
+P=packages/cultmath/tools
+python3 - <<'PY'
+p='packages/cultmath/tools/device/run-lavapipe.sh'
+s=open(p).read()
+k='python3 "$DEV/gen.py" "$W/work" "$CM"\n'
+s=s.replace(k,k+'sed -i -E "s/[.](cos|sin)([^A-Za-z0-9_])/._\\1\\2/g" "$W"/work/*.comp\n')
+open(p,'w').write(s)
+PY
+bash $P/glsl/build-glsl.sh /tmp/glslout >/dev/null
+GLSL_DIR=/tmp/glslout bash $P/device/run-lavapipe.sh 2>&1 | tail -4 || true
+set +e
+W=/tmp/device/work; R=/tmp/device
+DXC=$(find $R/dxc -name dxc -type f | head -1); export LD_LIBRARY_PATH=$(dirname $DXC)/../lib:$(dirname $DXC)
+CM=packages/cultmath
+for d in plain ncod gis; do mkdir -p $R/$d/lavapipe-hlsl $R/$d/lavapipe-glsl; done
+while IFS=$'\t' read -r tag _ _ n _ wout; do
+ spirv-dis --raw-id $W/$tag.g.spv -o /tmp/g.dis; python3 /tmp/nc.py /tmp/g.dis /tmp/g.nc.dis >/dev/null; spirv-as --target-env vulkan1.2 /tmp/g.nc.dis -o /tmp/g.nc.spv
+ $DXC -T cs_6_0 -E main -HV 2021 -spirv -fspv-target-env=vulkan1.2 -Od -I $CM/shaders $W/$tag.hlsl -Fo /tmp/hOd.spv >/dev/null 2>&1
+ spirv-dis --raw-id /tmp/hOd.spv -o /tmp/hOd.dis; python3 /tmp/nc.py /tmp/hOd.dis /tmp/hOd.nc.dis >/dev/null; spirv-as --target-env vulkan1.2 /tmp/hOd.nc.dis -o /tmp/hOd.nc.spv
+ $DXC -T cs_6_0 -E main -HV 2021 -spirv -fspv-target-env=vulkan1.2 -Gis -I $CM/shaders $W/$tag.hlsl -Fo /tmp/hGis.spv >/dev/null 2>&1
+ spirv-dis --raw-id /tmp/hGis.spv -o /tmp/hGis.dis; python3 /tmp/nc.py /tmp/hGis.dis /tmp/hGis.nc.dis >/dev/null; spirv-as --target-env vulkan1.2 /tmp/hGis.nc.dis -o /tmp/hGis.nc.spv
+ cp $R/results/lavapipe-hlsl/$tag.out $R/plain/lavapipe-hlsl/; cp $R/results/lavapipe-glsl/$tag.out $R/plain/lavapipe-glsl/
+ $R/vkrun /tmp/hOd.nc.spv $W/$tag.in $R/ncod/lavapipe-hlsl/$tag.out $n $wout >/dev/null
+ $R/vkrun /tmp/g.nc.spv $W/$tag.in $R/ncod/lavapipe-glsl/$tag.out $n $wout >/dev/null
+ $R/vkrun /tmp/hGis.nc.spv $W/$tag.in $R/gis/lavapipe-hlsl/$tag.out $n $wout >/dev/null
+ cp $R/ncod/lavapipe-glsl/$tag.out $R/gis/lavapipe-glsl/
+ for d in plain ncod gis; do cmp -s $R/$d/lavapipe-hlsl/$tag.out $R/$d/lavapipe-glsl/$tag.out || echo "EQ-FAIL $d $tag"; done
+done <$W/manifest.txt
+export CULTMATH_DEVICE_WORK=$W CULTMATH_DEVICE_NAME=$(sort -u $R/device.txt | head -1 | sed 's/^device=//') CULTMATH_DEVICE_IDENTITY=x CULTMATH_WRITE_DEVICE_BOUNDS=1
+B=packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
+for v in plain ncod gis; do
+  export CULTMATH_DEVICE_RESULTS=$R/$v
+  dotnet test packages/cultmath/tests/CultMath.Tests --no-build --filter "FullyQualifiedName~GlslMirrorTests.DeviceResultsHoldFixture" >/tmp/judge.$v.log 2>&1 || true
+  grep -aE "Error Message" -A8 /tmp/judge.$v.log | head -14; ls -la $B; cp $B /tmp/bounds.$v; echo "judge $v: $(tail -3 /tmp/judge.$v.log | tr '\n' ' ')"
+done
+for v in plain ncod gis; do awk -F'\t' -v v=$v '{k=$1; u[k]+=$5; if($5+0>m[k]+0)m[k]=$5; c[k]++} END{for(k in c) print "BOUNDS",v,k,"families",c[k],"maxulp",m[k],"sumulp",u[k]}' /tmp/bounds.$v; done
+for v in plain ncod; do awk -F'\t' '{print $1"/"$2"\t"$5}' /tmp/bounds.$v | sort > /tmp/b.$v; done
+join -t$'\t' /tmp/b.plain /tmp/b.ncod | awk -F'\t' '$2!=$3{print "ULPDIFF",$1,"plain",$2,"ncod",$3}' | head -60

From 3cd6815575ba3e8efba07ace6c372b616c6105b0 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 15:55:03 +0200
Subject: [PATCH 02/21] Research: variable-length shader inputs (array+count vs
 macro vs constants), for shader-lattice-loop; map section shader-lattice-loop

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 docs/cultmath-interval-ground-cut.md          |  20 ++++
 docs/research/shader-variable-inputs.md       | 111 ++++++++++++++++++
 .../shader-variable-inputs/entry-cbuffer.hlsl |  15 +++
 .../shader-variable-inputs/entry.comp.tail    |  16 +++
 .../shader-variable-inputs/entry.hlsl         |  16 +++
 docs/research/shader-variable-inputs/judge.py |  14 +++
 .../shader-variable-inputs/lattice-array.hlsl |   7 ++
 .../macro-accessor.hlsl                       |  12 ++
 docs/research/shader-variable-inputs/probe.sh |  55 +++++++++
 .../shader-variable-inputs/prototype.hlsl     |  75 ++++++++++++
 .../shader-variable-inputs/ref/Program.cs     |  50 ++++++++
 .../shader-variable-inputs/ref/Ref.csproj     |   4 +
 12 files changed, 395 insertions(+)
 create mode 100644 docs/research/shader-variable-inputs.md
 create mode 100644 docs/research/shader-variable-inputs/entry-cbuffer.hlsl
 create mode 100644 docs/research/shader-variable-inputs/entry.comp.tail
 create mode 100644 docs/research/shader-variable-inputs/entry.hlsl
 create mode 100644 docs/research/shader-variable-inputs/judge.py
 create mode 100644 docs/research/shader-variable-inputs/lattice-array.hlsl
 create mode 100644 docs/research/shader-variable-inputs/macro-accessor.hlsl
 create mode 100644 docs/research/shader-variable-inputs/probe.sh
 create mode 100644 docs/research/shader-variable-inputs/prototype.hlsl
 create mode 100644 docs/research/shader-variable-inputs/ref/Program.cs
 create mode 100644 docs/research/shader-variable-inputs/ref/Ref.csproj

diff --git a/docs/cultmath-interval-ground-cut.md b/docs/cultmath-interval-ground-cut.md
index 8e86b70e..16de3bcf 100644
--- a/docs/cultmath-interval-ground-cut.md
+++ b/docs/cultmath-interval-ground-cut.md
@@ -2461,3 +2461,23 @@ and 16:50 UTC (18:30 to 18:50 CEST). Logs are in the Imagination scratchpad
    It settles `span-allowance-gpu-margin`'s six CPU survivors, `iv-exp-gpu-widening`'s measurement and
    `device-p2-pin-notes`, and closes `glsl-browser-parity-run` and `affine-device-runner-seed`. It waits
    on 2b, because a capture of the old lowering goes stale at the switch.
+
+### shader-lattice-loop (follow-ups `shader-weighted-lattice-loop`, `lattice-shader-pins`)
+
+Written by Imagination (agent `imagination-ag4-shader-loop`, session `self-2026-10-16-ag4`) against `origin/main`
+`e2051c5a` and the build branch at `23ac4e89`. Research and probes: `docs/research/shader-variable-inputs.md`.
+Spec: `cultmath-tapes:cut_spec:cut-shader-lattice-loop.r1`. Question: `shader-site-capacity` (gates the spec).
+
+- **Bodies reach the shader as `float4 sites[CULTMATH_MAX_SITES]` plus `int count`, by value.** A caller accessor
+  macro cannot survive the library build (the built GLSL has no consumer macros), and library-owned uniforms would
+  take a binding the consumer owns. dxc, the SPIR-V edit, SPIRV-Cross and a WebGL2-style uniform-array consumer all
+  accept the array form (probes P1-P3).
+- **The shader owns the whole search.** `cultmath_weighted_lattice_cells` and `cultmath_power_border` replace the two
+  comment recipes; the four steps stay public. The box pass recomputes distances (no shader cache), the ring loop is
+  bounded by 37 with C#'s exit.
+- **The lavapipe run kills the exit and the normaliser** (probe table, research section 3): M1-M6 fail the C# device
+  judge; M7, a late exit, is equivalent by the window-independence proof. M1 needs several far-ring points.
+- **Smooth-step cap point** joins its family (m = f1 + smoothing, d past it, smoothing >= 0.5).
+- **Yggdrasil's sdk:10.0 Ubuntu image owns `glsl-parity.json`'s platform values** with the lavapipe bounds; a write
+  on another OS is refused.
+- Left: `shader-span-functions-array-form` (power_cells, multiplicative_cells, soft_gabriel_gate array forms).
diff --git a/docs/research/shader-variable-inputs.md b/docs/research/shader-variable-inputs.md
new file mode 100644
index 00000000..c8ea3296
--- /dev/null
+++ b/docs/research/shader-variable-inputs.md
@@ -0,0 +1,111 @@
+# Shader variable-length inputs: how shader libraries take a span, and what CultMath's build route allows
+
+For `cultmath-tapes:follow_up:shader-weighted-lattice-loop` and `cultmath-tapes:follow_up:lattice-shader-pins` (campaign `cultmath-tapes`).
+Imagination pass, agent `imagination-ag4-shader-loop`, session `self-2026-10-16-ag4`, 2026-10-17, against CultLib `origin/main` `e2051c5a`
+and the build branch `hands/cultmath-glsl-build-dxc` `23ac4e89`. Probes are in `docs/research/shader-variable-inputs/`.
+
+Tags: [src] primary source text read this pass; [web] search summary only; [probe] run this pass, output quoted below.
+
+## 1. The question
+
+C#'s `weighted_lattice_cells` reads the body span once per lattice cell (the weight is the exact power border of the
+cell centre), and the ring search around it is the part a consumer cannot safely write by hand: the exit bound,
+the two passes and the box-independent fold order. The shader port has the four steps only. A shader function cannot
+take `ReadOnlySpan`, the library targets GLSL ES 3.00 fragment shaders (WebGL2: no storage buffers), and the GLSL is
+built from the HLSL by dxc `lib_6_3` SPIR-V plus SPIRV-Cross (ruling `glsl-es-via-dxc-spirv-cross`).
+So how do bodies reach a shader `weighted_lattice_cells`?
+
+## 2. Prior art: how shader code that ships as a library takes a variable number of inputs
+
+- [src] Unity URP (`ShaderLibrary/Input.hlsl`, `RealtimeLights.hlsl`, Graphics `master`): a fixed capacity
+  `MAX_VISIBLE_LIGHTS` chosen per platform (`MAX_VISIBLE_LIGHT_COUNT_LOW_END_MOBILE` under `SHADER_API_GLES30`,
+  `_MOBILE` for GLES3/WebGPU, `_DESKTOP` otherwise), constant-buffer arrays `float4 _AdditionalLightsPosition[MAX_VISIBLE_LIGHTS]`
+  and the like, with `StructuredBuffer<LightData>` only behind `USE_STRUCTURED_BUFFER_FOR_LIGHT_DATA` (defined 0). The
+  count is a uniform read through `GetAdditionalLightsCount()`, and `GetAdditionalLight(uint i, float3 positionWS)` is
+  the accessor; `LIGHT_LOOP_BEGIN(lightCount)` / `LIGHT_LOOP_END` macros hide the cluster versus plain loop. The
+  pipeline owns the storage and the accessor; user shaders call them. Capacity plus count, storage owned by the include.
+- [src] Filament (`shaders/src/surface_light_punctual.fs`, `main`): the loop is the engine's, over a froxel record
+  (`froxelsUniforms.records`, then `froxelRecordUniforms.records`) giving `recordOffset` and `count`; each light is
+  `lightsUniforms.lights[lightIndex]`, a uniform-block array. Material code never sees the loop. The engine owns both
+  the storage and the loop because it also owns the uniform layout.
+- [src] three.js (`ShaderChunk/lights_fragment_begin.glsl.js`, `dev`): `for ( int i = 0; i < NUM_POINT_LIGHTS; i ++ )`
+  under `#pragma unroll_loop_start`, reading `pointLights[ i ]`; `NUM_POINT_LIGHTS` is a define the renderer writes,
+  so the shader is regenerated per light count. Count as a compile-time constant; the library is source text.
+- [web] Bevy: clustered forward needs storage buffers; on WebGL2 it falls back to a uniform buffer with a capped
+  object count (`MAX_UNIFORM_BUFFER_CLUSTERABLE_OBJECTS` 204 in an older `bevy_pbr`, asserted to fit 16384 bytes; the
+  Many Lights example says 256 lights under `WGPU_SETTINGS_PRIO=webgl2`). Capacity plus count where storage is absent.
+- [web] lygia (README conventions, via search): reuse by `#ifndef` / `#define` options the caller sets before the
+  include (`SAMPLER_FNC(TEX, UV)`, `MYFUNC_TYPE`, per-function sampler overrides). Caller-supplied accessor macros; the
+  library ships as source text, which is what lets a macro reach inside a function body.
+
+The pattern that splits them: a caller-supplied accessor (lygia, URP's accessor functions, three.js's define) works
+where the library is source text the caller's preprocessor sees. Where the library is compiled or its storage layout is
+fixed (URP's GLES path, Bevy's WebGL2 fallback, Filament's uniform blocks), the input is a fixed-capacity array plus a
+count, and the capacity is a named library constant.
+
+## 3. What the build route allows (probes)
+
+| Candidate | HLSL (dxc) | Library SPIR-V and SPIRV-Cross GLSL | C# mirror (`TransformHlslToCSharp`) | Verdict |
+|---|---|---|---|---|
+| Fixed-size array parameter plus count | compiles, `lib_6_3` and `cs_6_0` [probe P1, P3] | see P2 | needs one transform (`T x[N]` parameter to `T[] x`) | see section 4 |
+| Caller accessor macro (`CULTMATH_BODY(i)`) | the library build defines no accessor, so the function is absent [probe P4] | absent from the built GLSL: SPIRV-Cross output carries no consumer macro | the mirror would need the macro too | refused by the route |
+| Bodies packed into library-owned constants | a library cbuffer or uniform | a uniform block in a function-only library; a binding the consumer does not own | a static field | refused (P5, by construction, not run): a library may not own a consumer's binding |
+
+Probes (files in `shader-variable-inputs/`):
+
+- [probe] P1, local, dxc 2026_07_29 (`.tools/dxc`): `lattice-array.hlsl` (CultMath.hlsl, `prototype.hlsl`, one export)
+  compiles with `-T lib_6_3 -HV 2021 -spirv -fspv-target-env=universal1.5 -Od`. The SPIR-V types the array as
+  `OpTypeArray %v4float %uint_16` behind a Function pointer, and `-Od` copies it at each call (`param_var_bodies`).
+- [probe] P3, local: `entry-cbuffer.hlsl` passes a cbuffer array directly and a `StructuredBuffer` copied into a local
+  array; both compile to SPIR-V (`cs_6_0`) and to DXIL.
+- [probe] P4, local: `macro-accessor.hlsl` with no `CULTMATH_BODY` defined fails, `use of undeclared identifier`: a
+  macro-parameterised function does not exist in a library compiled without the caller's macros, so the built GLSL
+  cannot carry it. Shipping it would need a hand-kept GLSL text beside the build, a second owner the ruling removed.
+- [probe] P2, Yggdrasil job (`probe.sh` at `23ac4e89`, sdk:10.0, 2026-10-17): with the prototype appended to
+  `CultMath.hlsl` and two build-tool edits (`wrappers.py` strips `[N]` from an argument name; `partition.py` accepts
+  `static const int`), `build-glsl.sh` is green ("build shape ok", "suffixed ids: 0; inout: 0") and emits
+  `const int CULTMATH_MAX_SITES = 16;`, `vec4 cultmath_power_border(vec3 p, vec4 sites[16], int count)` and
+  `vec4 cultmath_weighted_lattice_cells(vec2 p, float time, vec4 bodies[16], int count, ...)`. A `#version 300 es`
+  fragment consumer passing `uniform vec4 zone[CULTMATH_MAX_SITES]` compiles with glslang.
+- [probe] Same job, lavapipe (`llvmpipe (LLVM 20.1.2, 256 bits)`), 257 cases from `ref/Program.cs` (the ring-17 point
+  of `TheCapIsReachedAndMatchesTheFullBox` and 7 neighbours, four looks, five normals including (3e-30, -4e-30) and
+  (1e30, 2e30), a zero normal at stretch 1, counts 0, 1, 3, 6, 16), judged against C#'s bits at 2.2e-6 max(|v|, 1):
+
+| Variant (HLSL route unless named) | bit-exact | over bound | worst |
+|---|---|---|---|
+| built GLSL | 237 | 0 | 1.19e-6 |
+| HLSL (equal to built GLSL bit for bit) | 237 | 0 | 1.19e-6 |
+| M1 exit at `0.5 k` | 236 | 1 | 4.28e-3 |
+| M2 exit ignores the smooth band (`>= f2`) | 226 | 13 | 8.33e-2 |
+| M3 normaliser drops the divide by the largest component | 148 | 96 | 1e30 |
+| M4 normaliser drops the divide by length | 1 | 208 | 0.259 |
+| M5 smooth step loses its `min` cap | 153 | 85 | 2.26e-3 |
+| M6 box pass skips its first row | 228 | 9 | 0.807 |
+| M7 exit one ring late (`0.5 (k - 2)`) | 237 | 0 | 1.19e-6 |
+
+M7 is equivalent: the result does not depend on the box (the proof above `weighted_lattice_cells`), so a late exit
+costs rings and changes nothing. M1 is killed by one case of 257, the ring-17 point: an early exit only matters where
+a far ring wins, so the device family must carry several such points.
+
+## 4. Decision
+
+The fixed-size array plus count is the only candidate the route admits, and it is the shape the compiled-library
+prior art uses (URP's GLES path, Bevy's WebGL2 fallback, Filament's uniform blocks). The capacity is a named library
+constant, `CULTMATH_MAX_SITES`, shared by every span-taking shader function. Its value is
+`cultmath-tapes:question:shader-site-capacity` (Aetheria zones: p50 17, p99 57, max 80 bodies, gravity map B28).
+
+The shader recomputes each distance in the box pass instead of caching it: C#'s 75 x 75 stack cache is not a shader
+option, and recomputing gives the same value, as the probe's bit-exact HLSL and built-GLSL agreement shows.
+Reflection cannot pass a `ReadOnlySpan`, so the mirror and the fixture reach the C# span functions through one
+explicit adapter table rather than `MethodInfo.Invoke`.
+
+## 5. lattice-shader-pins
+
+- The smooth-step family draws m in [f1, f1 + smoothing), so the cap never binds. The cap binds when m = f1 + smoothing,
+  d = f1 + x smoothing with x around 1.3 to 1.9, and smoothing above about 0.25: next - m = (d - m) h - h (1 - h)
+  smoothing / (1 + 3 smoothing) is positive there (for smoothing 1 and d - m = 0.5, h = 0.156 and next - m = +0.045).
+  M5 above is killed by the whole function already; the step family should kill it on its own.
+- Platform values: `8b31e47e` rewrote 7 platform-family entries of `glsl-parity.json` from "Ubuntu 24.04.5 LTS" to
+  "Microsoft Windows 10.0.26200", while `7ddb1040` recorded the lavapipe bounds on Yggdrasil against that fixture.
+  The bounds, the lavapipe job and the build route all run in Yggdrasil's sdk:10.0 Ubuntu image, so that image
+  owns the fixture's platform values too. A write on another OS is refused rather than reviewed.
diff --git a/docs/research/shader-variable-inputs/entry-cbuffer.hlsl b/docs/research/shader-variable-inputs/entry-cbuffer.hlsl
new file mode 100644
index 00000000..7e6ced39
--- /dev/null
+++ b/docs/research/shader-variable-inputs/entry-cbuffer.hlsl
@@ -0,0 +1,15 @@
+// Probe C: a compute entry passing a constant-buffer array, and one passing a StructuredBuffer copied to a local array.
+#include "lattice-array.hlsl"
+cbuffer Zone : register(b0) { float4 zoneBodies[CULTMATH_MAX_SITES]; int zoneCount; };
+StructuredBuffer<float4> bufferBodies : register(t1);
+RWStructuredBuffer<float4> result : register(u2);
+[numthreads(64, 1, 1)]
+void main(uint3 id : SV_DispatchThreadID)
+{
+    float2 p = float2(id.x * 7.0, id.y * 11.0);
+    float4 local[CULTMATH_MAX_SITES];
+    for (int i = 0; i < CULTMATH_MAX_SITES; i++)
+        local[i] = i < zoneCount ? bufferBodies[i] : float4(0.0, 0.0, 0.0, 1.0);
+    result[id.x] = cultmath_weighted_lattice_cells(p, 1.0, zoneBodies, zoneCount, 260.0, 0.3, 1.6, 120.0, 0.35, float2(1.0, 2.0), 1.5)
+        + cultmath_weighted_lattice_cells(p, 1.0, local, zoneCount, 260.0, 0.3, 1.6, 120.0, 0.35, float2(1.0, 2.0), 1.5);
+}
diff --git a/docs/research/shader-variable-inputs/entry.comp.tail b/docs/research/shader-variable-inputs/entry.comp.tail
new file mode 100644
index 00000000..c6713929
--- /dev/null
+++ b/docs/research/shader-variable-inputs/entry.comp.tail
@@ -0,0 +1,16 @@
+layout(local_size_x = 64) in;
+layout(std430, binding = 0) readonly buffer IB { uint a[]; } In;
+layout(std430, binding = 1) buffer OB { uint a[]; } Out;
+void main()
+{
+    uint i = gl_GlobalInvocationID.x; if (i >= NCASES) return; uint b = i * 76u;
+    vec4 bodies[CULTMATH_MAX_SITES];
+    for (int k = 0; k < CULTMATH_MAX_SITES; k++)
+        bodies[k] = uintBitsToFloat(uvec4(In.a[b + 2u + 4u * uint(k)], In.a[b + 3u + 4u * uint(k)], In.a[b + 4u + 4u * uint(k)], In.a[b + 5u + 4u * uint(k)]));
+    uint c = b + 67u;
+    vec4 r = cultmath_weighted_lattice_cells(uintBitsToFloat(uvec2(In.a[b], In.a[b + 1u])), uintBitsToFloat(In.a[c]), bodies, int(In.a[b + 66u]),
+        uintBitsToFloat(In.a[c + 1u]), uintBitsToFloat(In.a[c + 2u]), uintBitsToFloat(In.a[c + 3u]), uintBitsToFloat(In.a[c + 4u]),
+        uintBitsToFloat(In.a[c + 5u]), uintBitsToFloat(uvec2(In.a[c + 6u], In.a[c + 7u])), uintBitsToFloat(In.a[c + 8u]));
+    uvec4 w = floatBitsToUint(r);
+    Out.a[i * 4u] = w.x; Out.a[i * 4u + 1u] = w.y; Out.a[i * 4u + 2u] = w.z; Out.a[i * 4u + 3u] = w.w;
+}
diff --git a/docs/research/shader-variable-inputs/entry.hlsl b/docs/research/shader-variable-inputs/entry.hlsl
new file mode 100644
index 00000000..91b21046
--- /dev/null
+++ b/docs/research/shader-variable-inputs/entry.hlsl
@@ -0,0 +1,16 @@
+// Probe compute entry (HLSL route): 76 words in per case (p, 16 bodies, count, 9 parameters), 4 words out.
+#include "CultMath.hlsl"
+[[vk::binding(0)]] StructuredBuffer<uint> In;
+[[vk::binding(1)]] RWStructuredBuffer<uint> Out;
+[numthreads(64, 1, 1)] void main(uint3 id : SV_DispatchThreadID)
+{
+    uint i = id.x; if (i >= NCASES) return; uint b = i * 76u;
+    float4 bodies[CULTMATH_MAX_SITES];
+    for (int k = 0; k < CULTMATH_MAX_SITES; k++)
+        bodies[k] = float4(asfloat(In[b + 2 + 4 * k]), asfloat(In[b + 3 + 4 * k]), asfloat(In[b + 4 + 4 * k]), asfloat(In[b + 5 + 4 * k]));
+    uint c = b + 67u;
+    float4 r = cultmath_weighted_lattice_cells(float2(asfloat(In[b]), asfloat(In[b + 1])), asfloat(In[c]), bodies, asint(In[b + 66]),
+        asfloat(In[c + 1]), asfloat(In[c + 2]), asfloat(In[c + 3]), asfloat(In[c + 4]), asfloat(In[c + 5]),
+        float2(asfloat(In[c + 6]), asfloat(In[c + 7])), asfloat(In[c + 8]));
+    Out[i * 4] = asuint(r.x); Out[i * 4 + 1] = asuint(r.y); Out[i * 4 + 2] = asuint(r.z); Out[i * 4 + 3] = asuint(r.w);
+}
diff --git a/docs/research/shader-variable-inputs/judge.py b/docs/research/shader-variable-inputs/judge.py
new file mode 100644
index 00000000..97b23985
--- /dev/null
+++ b/docs/research/shader-variable-inputs/judge.py
@@ -0,0 +1,14 @@
+#!/usr/bin/env python3
+"""Compare a device output with C#'s reference bits: cases over the lavapipe bound 2.2e-6 max(|v|, 1), and the largest.
+usage: judge.py <ref.bin> <out.bin> <label>"""
+import math, struct, sys
+ref, out = open(sys.argv[1], 'rb').read(), open(sys.argv[2], 'rb').read()
+n = len(ref) // 16
+r, o = struct.unpack('<%df' % (4 * n), ref), struct.unpack('<%df' % (4 * n), out)
+over, exact, worst = 0, 0, 0.0
+for i in range(n):
+    s = max((abs(o[4*i+j] - r[4*i+j]) / max(abs(r[4*i+j]), 1.0) if math.isfinite(o[4*i+j]) else math.inf) for j in range(4))
+    exact += ref[16*i:16*i+16] == out[16*i:16*i+16]
+    over += s > 2.2e-6
+    worst = max(worst, s)
+print('%s: cases %d, bit-exact %d, over 2.2e-6 %d, worst %.3g' % (sys.argv[3], n, exact, over, worst))
diff --git a/docs/research/shader-variable-inputs/lattice-array.hlsl b/docs/research/shader-variable-inputs/lattice-array.hlsl
new file mode 100644
index 00000000..03028f00
--- /dev/null
+++ b/docs/research/shader-variable-inputs/lattice-array.hlsl
@@ -0,0 +1,7 @@
+// Probe A (local dxc): the prototype as a lib_6_3 SPIR-V library export, bodies as a fixed-size array parameter plus a count.
+#include "CultMath.hlsl"
+#include "prototype.hlsl"
+export float4 probe_lattice(float2 p, float4 bodies[CULTMATH_MAX_SITES], int count)
+{
+    return cultmath_weighted_lattice_cells(p, 1.0, bodies, count, 260.0, 0.3, 1.6, 120.0, 0.35, float2(1.0, 2.0), 1.5);
+}
diff --git a/docs/research/shader-variable-inputs/macro-accessor.hlsl b/docs/research/shader-variable-inputs/macro-accessor.hlsl
new file mode 100644
index 00000000..d98163f5
--- /dev/null
+++ b/docs/research/shader-variable-inputs/macro-accessor.hlsl
@@ -0,0 +1,12 @@
+// Probe B: bodies through a caller-supplied accessor macro. The library build defines no accessor.
+#include "CultMath.hlsl"
+#ifdef CULTMATH_BODY
+float4 cultmath_power_border_m(float3 p)
+{
+    float4 border = float4(0.0, 0.0, 0.0, 1.0e30);
+    for (int k = 1; k < CULTMATH_BODY_COUNT; k++)
+        border = cultmath_power_border_step(p, CULTMATH_BODY(0), CULTMATH_BODY(k), border);
+    return border;
+}
+#endif
+export float4 probe_macro(float3 p) { return cultmath_power_border_m(p); }
diff --git a/docs/research/shader-variable-inputs/probe.sh b/docs/research/shader-variable-inputs/probe.sh
new file mode 100644
index 00000000..a5acbb5d
--- /dev/null
+++ b/docs/research/shader-variable-inputs/probe.sh
@@ -0,0 +1,55 @@
+#!/usr/bin/env bash
+# Probe for shader-weighted-lattice-loop: the prototype through the dxc + SPIRV-Cross build and on lavapipe, against C#.
+# Run from a CultLib clone at a revision with packages/cultmath/tools/glsl/build-glsl.sh (hands/cultmath-glsl-build-dxc
+# 23ac4e89), inside mcr.microsoft.com/dotnet/sdk:10.0, with this directory at $P. The clone is disposable: the
+# prototype is appended to its CultMath.hlsl, and two build-tool lines are patched (array arguments, int constants).
+set -euo pipefail
+P=${P:-/tmp/probe}; ROOT=$(pwd); CM=$ROOT/packages/cultmath; W=/tmp/pw; mkdir -p $W
+apt-get update -qq >/dev/null && apt-get install -y -qq --no-install-recommends python3 >/dev/null
+cat $P/prototype.hlsl >> $CM/shaders/CultMath.hlsl
+python3 - $CM/tools/glsl/wrappers.py <<'PY'
+import sys; f = sys.argv[1]; t = open(f).read()
+t = t.replace(r"args = [re.split(r'\s+', p)[-1] for p in params]", r"args = [re.split(r'\s+', re.sub(r'\[.*\]', '', p))[-1] for p in params]")
+open(f, 'w').write(t)
+PY
+grep -c "re.sub(r'" $CM/tools/glsl/wrappers.py
+python3 - $CM/tools/glsl/partition.py <<'PY'
+import sys; f = sys.argv[1]; t = open(f).read()
+t = t.replace(r"r'^static const float (CULTMATH_\w+) = (-?\d+(?:\.\d*)?(?:[eE][+-]?\d+)?);$'", r"r'^static const (float|int) (CULTMATH_\w+) = (-?\d+(?:\.\d*)?(?:[eE][+-]?\d+)?);$'")
+t = t.replace("consts[o].append('const float %s = %s;' % m.groups())", "consts[o].append('const %s %s = %s;' % m.groups())")
+open(f, 'w').write(t)
+PY
+grep -c "(float|int)" $CM/tools/glsl/partition.py
+echo "== build"
+bash $CM/tools/glsl/build-glsl.sh $W/built 2>&1 | tail -12
+echo "== array functions in the built core.glsl"
+grep -nE "^(const int CULTMATH_MAX_SITES|vec4 cultmath_power_border\(|float cultmath_lattice_cell_distance\(|vec4 cultmath_weighted_lattice_cells\()" $W/built/core.glsl
+echo "== ES 3.00 fragment consumer passing a uniform array"
+{ printf '#version 300 es\nprecision highp float;\nprecision highp int;\n'; cat $W/built/core.glsl
+  printf 'uniform vec4 zone[CULTMATH_MAX_SITES];\nuniform int zoneCount;\nout highp vec4 c;\nvoid main() { c = cultmath_weighted_lattice_cells(gl_FragCoord.xy, 1.0, zone, zoneCount, 260.0, 0.7, 1.6, 120.0, 0.35, vec2(0.6, 0.8), 1.5); }\n'; } > $W/consumer.frag
+glslangValidator $W/consumer.frag && echo "consumer ES 3.00 ok"
+echo "== lavapipe"
+apt-get install -y -qq --no-install-recommends mesa-vulkan-drivers libvulkan-dev gcc libc6-dev >/dev/null
+gcc -O2 -o $W/vkrun $CM/tools/device/vkrun.c -lvulkan
+cp -r $P/ref $W/ref && sed -i 's#../../../../packages#'"$CM"'/..#' $W/ref/Ref.csproj
+N=$(dotnet run --project $W/ref -c Release -- $W/in.bin $W/ref.bin | tail -1); echo "cases $N"
+DXC=$(find $CM/.tools/glsl/dxc -name dxc -type f | head -1); export LD_LIBRARY_PATH=$(dirname $DXC)/../lib:$(dirname $DXC)
+{ printf '#version 310 es\nprecision highp float;\nprecision highp int;\n#define NCASES %su\n' $N; cat $W/built/core.glsl $P/entry.comp.tail; } > $W/e.comp
+glslangValidator -V --target-env vulkan1.2 -o $W/g.spv $W/e.comp >$W/g.log || { head $W/g.log; exit 1; }
+$W/vkrun $W/g.spv $W/in.bin $W/g.out $N 4
+python3 $P/judge.py $W/ref.bin $W/g.out built-glsl
+run_hlsl() {  # $1 label, $2 sed expression applied to a copy of the shaders
+  rm -rf $W/s && cp -r $CM/shaders $W/s && sed -i "$2" $W/s/CultMath.hlsl
+  $DXC -T cs_6_0 -E main -HV 2021 -spirv -fspv-target-env=vulkan1.2 -D NCASES=${N}u -I $W/s $P/entry.hlsl -Fo $W/h.spv >$W/h.log 2>&1 || { head -5 $W/h.log; exit 1; }
+  $W/vkrun $W/h.spv $W/in.bin $W/h.out $N 4 >/dev/null
+  python3 $P/judge.py $W/ref.bin $W/h.out "$1"
+}
+run_hlsl hlsl 's/^$//'
+cmp $W/h.out $W/g.out && echo "hlsl equals built glsl bit for bit" || echo "hlsl and built glsl differ (plain form; the gate is strict form)"
+run_hlsl "M1 exit at 0.5k" 's/0\.5 \* (k - 1) >= max/0.5 * k >= max/'
+run_hlsl "M2 exit ignores the smooth band" 's/>= max(f2, f1 + 2\.0 \* smoothing))$/>= f2)/'
+run_hlsl "M3 normaliser drops the pre-scale" 's/normal = stretchNormal \/ scale;/normal = stretchNormal;/'
+run_hlsl "M4 normaliser drops the length" 's/normal = normal \/ length(normal);//'
+run_hlsl "M5 smooth step loses its cap" 's/return min(next, f1 + smoothing);/return next;/'
+run_hlsl "M6 box pass skips its first row" 's/for (int dz = -reach; dz <= reach; dz++)/for (int dz = -reach + 1; dz <= reach; dz++)/'
+run_hlsl "M7 late exit (equivalent: window-independent)" 's/0\.5 \* (k - 1) >= max/0.5 * (k - 2) >= max/'
diff --git a/docs/research/shader-variable-inputs/prototype.hlsl b/docs/research/shader-variable-inputs/prototype.hlsl
new file mode 100644
index 00000000..9e126ef9
--- /dev/null
+++ b/docs/research/shader-variable-inputs/prototype.hlsl
@@ -0,0 +1,75 @@
+// The prototype, appended to CultMath.hlsl by probe.sh: the whole weighted_lattice_cells with bodies as a fixed-size array and a count.
+static const int CULTMATH_MAX_SITES = 16;
+
+float4 cultmath_power_border(float3 p, float4 sites[CULTMATH_MAX_SITES], int count)
+{
+    CultSiteCells cells = cultmath_site_cells_empty();
+    for (int i = 0; i < count; i++)
+        cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
+    float4 border = float4(0.0, 0.0, 0.0, 1.0e30);
+    int owner = (int)cells.nearestSite;
+    if (owner < 0)
+        return border;
+    for (int k = 0; k < count; k++)
+        if (k != owner)
+            border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+    return border;
+}
+
+float cultmath_lattice_cell_distance(float2 q, float2 cell, float time, float drift, float4 bodies[CULTMATH_MAX_SITES], int count,
+    float cellSize, float boost, float falloff, float2 normal, float stretch)
+{
+    float3 site = cultmath_lattice_site(cell, time, drift);
+    float border = cultmath_power_border(float3((cell + 0.5) * cellSize, 0.0), bodies, count).w;
+    return cultmath_lattice_distance(q, site.xy, cultmath_lattice_weight(site.z, border, boost, falloff), normal, stretch);
+}
+
+float4 cultmath_weighted_lattice_cells(float2 p, float time, float4 bodies[CULTMATH_MAX_SITES], int count, float cellSize, float drift,
+    float boost, float falloff, float smoothing, float2 stretchNormal, float stretch)
+{
+    float scale = max(abs(stretchNormal.x), abs(stretchNormal.y));
+    float2 normal = float2(1.0, 0.0);
+    if (scale > 0.0)
+    {
+        normal = stretchNormal / scale;
+        normal = normal / length(normal);
+    }
+    float2 q = p / cellSize;
+    float2 origin = floor(q);
+    int cx0 = (int)origin.x;
+    int cz0 = (int)origin.y;
+    float f1 = 1.0e30;
+    float f2 = 1.0e30;
+    int reach = 0;
+    for (int k = 0; k <= 37; k++)
+    {
+        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+            break;
+        for (int dz = -k; dz <= k; dz++)
+        {
+            int step = dz == -k || dz == k || k == 0 ? 1 : 2 * k;
+            for (int dx = -k; dx <= k; dx += step)
+            {
+                float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+                if (d < f1) { f2 = f1; f1 = d; }
+                else if (d < f2) f2 = d;
+            }
+        }
+        reach = k;
+    }
+    float m = f1 + smoothing;
+    float best = 1.0e30;
+    float second = 1.0e30;
+    int winDx = 0;
+    int winDz = 0;
+    for (int dz = -reach; dz <= reach; dz++)
+        for (int dx = -reach; dx <= reach; dx++)
+        {
+            float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+            if (d < best) { second = best; best = d; winDx = dx; winDz = dz; }
+            else if (d < second) second = d;
+            m = cultmath_lattice_smooth_step(m, d, f1, smoothing);
+        }
+    int4 id = cultmath_pcg4d(int4(cx0 + winDx, cz0 + winDz, 0, 0));
+    return float4(best, second, m, (float)((uint)id.w >> 8) * (1.0 / 16777216.0));
+}
diff --git a/docs/research/shader-variable-inputs/ref/Program.cs b/docs/research/shader-variable-inputs/ref/Program.cs
new file mode 100644
index 00000000..b884f116
--- /dev/null
+++ b/docs/research/shader-variable-inputs/ref/Program.cs
@@ -0,0 +1,50 @@
+// Probe reference: writes the lattice cases (76 words each) and C#'s weighted_lattice_cells bits (4 words each).
+// usage: Ref <in.bin> <ref.bin>; prints the case count.
+using CultMath;
+using static CultMath.math;
+
+const int Max = 16;
+var cases = new List<(float2 p, float t, float4[] b, float cell, float drift, float boost, float falloff, float s, float2 n, float st)>();
+float4[] Bodies(float t, int count)
+{
+    var b = new float4[count];
+    for (var i = 0; i < count; i++)
+    {
+        var a = 0.001f * (i + 1) * t + i; var r = 300.0f + 220.0f * i;
+        b[i] = new float4(r * MathF.Cos(a), r * MathF.Sin(a), 0.0f, 40.0f + 40.0f * i);
+    }
+    return b;
+}
+// The ring-17 point of LatticeCellsTests.TheCapIsReachedAndMatchesTheFullBox, and its neighbours.
+for (var j = 0; j < 8; j++)
+    cases.Add((new float2(1446.7345f + 3.0f * j, -680.7637f), 97.69269f, Bodies(97.69269f, 6), 260.0f, 0.7f, 4.0f, 1.0e6f, 1.0f, new float2(0.6f, 0.8f), 2.0f));
+var looks = new[] { (1.6f, 1.0f, 0.35f), (1.6f, 2.0f, 0.35f), (4.0f, 2.0f, 1.0f), (0.0f, 1.0f, 0.05f) };
+var normals = new[] { new float2(0.6f, 0.8f), new float2(3.0f, 4.0f), new float2(3.0e-30f, -4.0e-30f), new float2(1.0e30f, 2.0e30f), new float2(-1.0f, 1.0e-3f) };
+var rng = new System.Random(20261017);
+float U(float a, float b) => a + (b - a) * (float)rng.NextDouble();
+for (var i = 0; i < 248; i++)
+{
+    var (boost, stretch, s) = looks[i % 4];
+    var n = normals[(i / 4) % normals.Length];
+    var count = new[] { 6, 0, 1, 16, 6, 3 }[(i / 20) % 6];
+    var t = U(0.0f, 200.0f);
+    cases.Add((new float2(U(-3000, 3000), U(-3000, 3000)), t, Bodies(t, count), 260.0f, 0.7f, boost, 120.0f, s, n, stretch));
+}
+// Zero normal at stretch 1 is (1, 0).
+cases.Add((new float2(10.0f, 20.0f), 1.0f, Bodies(1.0f, 6), 260.0f, 0.7f, 1.6f, 120.0f, 0.35f, new float2(0.0f, 0.0f), 1.0f));
+using var input = new BinaryWriter(File.Create(args[0]));
+using var reference = new BinaryWriter(File.Create(args[1]));
+foreach (var c in cases)
+{
+    input.Write(c.p.x); input.Write(c.p.y);
+    for (var k = 0; k < Max; k++)
+    {
+        var v = k < c.b.Length ? c.b[k] : new float4(0.0f, 0.0f, 0.0f, 0.0f);
+        input.Write(v.x); input.Write(v.y); input.Write(v.z); input.Write(v.w);
+    }
+    input.Write(c.b.Length);
+    foreach (var f in new[] { c.t, c.cell, c.drift, c.boost, c.falloff, c.s, c.n.x, c.n.y, c.st }) input.Write(f);
+    var r = weighted_lattice_cells(c.p, c.t, c.b, c.cell, c.drift, c.boost, c.falloff, c.s, c.n, c.st);
+    reference.Write(r.x); reference.Write(r.y); reference.Write(r.z); reference.Write(r.w);
+}
+Console.WriteLine(cases.Count);
diff --git a/docs/research/shader-variable-inputs/ref/Ref.csproj b/docs/research/shader-variable-inputs/ref/Ref.csproj
new file mode 100644
index 00000000..1aa23393
--- /dev/null
+++ b/docs/research/shader-variable-inputs/ref/Ref.csproj
@@ -0,0 +1,4 @@
+<Project Sdk="Microsoft.NET.Sdk">
+  <PropertyGroup><OutputType>Exe</OutputType><TargetFramework>net10.0</TargetFramework><Nullable>enable</Nullable><ImplicitUsings>enable</ImplicitUsings></PropertyGroup>
+  <ItemGroup><ProjectReference Include="../../../../packages/cultmath/src/CultMath/CultMath.csproj" /></ItemGroup>
+</Project>

From 150ea0a06016260485ed494a1a7a54579a112722 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:09:18 +0200
Subject: [PATCH 03/21] CultMath shaders: cultmath_power_border,
 cultmath_lattice_cell_distance and cultmath_weighted_lattice_cells over a
 fixed-capacity site array

CULTMATH_MAX_SITES defaults to 128 under #ifndef. The consumer-written ring-loop and border-loop comment recipes are deleted. The C# mirror takes the array as T[]; the span twins live in SiteArrays; the GLSL lowering keeps the capacity macro; gen.py learns the array leaf; the smooth-step family gains its cap-point draw; CULTMATH_WRITE_GLSL refuses non-Linux.

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/README.md                   |   5 +-
 packages/cultmath/docs/design.md              |  32 ++++-
 packages/cultmath/shaders/CultMath.hlsl       | 109 ++++++++++++---
 .../cultmath/src/CultMath/math.Lattice.cs     |   2 +-
 .../tests/CultMath.Tests/GlslLowering.cs      |   5 +-
 .../tests/CultMath.Tests/GlslMirrorTests.cs   |  30 +++-
 .../HlslSourceCompatibilityTests.cs           |  90 ++++++++++--
 .../tests/CultMath.Tests/LatticeCellsTests.cs |  22 +--
 .../tests/CultMath.Tests/SiteArrays.cs        | 129 ++++++++++++++++++
 packages/cultmath/tools/device/gen.py         |  14 ++
 .../Shaders/CultMath.hlsl                     | 109 ++++++++++++---
 11 files changed, 474 insertions(+), 73 deletions(-)
 create mode 100644 packages/cultmath/tests/CultMath.Tests/SiteArrays.cs

diff --git a/packages/cultmath/README.md b/packages/cultmath/README.md
index 29113254..086dd222 100644
--- a/packages/cultmath/README.md
+++ b/packages/cultmath/README.md
@@ -38,8 +38,9 @@ shader semantics.
   drifting lattice whose cell weights come from the exact power border of the body span at each cell centre, with a stretched
   metric and an exact ring search over the stated range (`LatticeMaxBoost`, `LatticeMaxStretch`, `LatticeMaxSmoothing`). It composes the
   public steps `lattice_site`, `lattice_weight`, `lattice_distance` and `lattice_smooth_step`. The shaders carry the four steps as
-  `cultmath_lattice_site`, `cultmath_lattice_weight`, `cultmath_lattice_distance` and `cultmath_lattice_smooth_step`; the ring and box loops
-  are the shader caller's, written as the comment above them in `CultMath.hlsl` gives them, and the argument checks become its preconditions.
+  `cultmath_lattice_site`, `cultmath_lattice_weight`, `cultmath_lattice_distance` and `cultmath_lattice_smooth_step`, and the whole function as `cultmath_weighted_lattice_cells(p, time, bodies,
+  count, ...)` over a `float4 bodies[CULTMATH_MAX_SITES]` array (128 by default; define the macro before including to change it);
+  `cultmath_power_border(p, sites, count)` is the matching border. The argument checks become the shader caller's preconditions.
 - `shaders/CultMath.hlsl`, a canonical HLSL mirror include for shader-side
   parity. HLSL already owns `float2`, `float3`, and `float4`; the include
   exposes `cultmath_*` functions for shared semantics HLSL does not provide.
diff --git a/packages/cultmath/docs/design.md b/packages/cultmath/docs/design.md
index d6abafd8..4e55dae4 100644
--- a/packages/cultmath/docs/design.md
+++ b/packages/cultmath/docs/design.md
@@ -95,7 +95,8 @@ and HLSL's one-based `_11`..`_33` element names.
 Roslyn against CultMath. These transformations are the complete list; if a body
 needs anything else, the test fails:
 
-1. Include guards (`#ifndef`/`#define`/`#endif`) are dropped.
+1. Include guards (`#ifndef`/`#define`/`#endif`) are dropped, except the capacity macro (`#ifndef CULTMATH_MAX_SITES`,
+   `#define CULTMATH_MAX_SITES 128`, `#endif`), which becomes `const int CULTMATH_MAX_SITES = 128;`.
 2. Functions taking `Texture2D`/`SamplerState` are dropped; GPU resources have
    no CultMath analog.
 3. File-scope `static const` becomes `const`.
@@ -103,7 +104,8 @@ needs anything else, the test fails:
 5. Struct fields gain `public`. HLSL struct members have no access-modifier
    concept; a C# struct's fields default to `private`, which would hide them
    from the mirror test's reflection-based field comparison.
-6. The file body is wrapped in a class, since C# has no free functions; HLSL
+6. An array parameter `T name[CULTMATH_MAX_SITES]` becomes `T[] name`.
+7. The file body is wrapped in a class, since C# has no free functions; HLSL
    functions become private instance methods.
 
 HLSL constructs that stay outside the target and must not appear in the mirror:
@@ -156,6 +158,10 @@ hand. Regenerate them, and the golden fixture
 $env:CULTMATH_WRITE_GLSL = "1"; dotnet test packages/cultmath/tests/CultMath.Tests --filter GlslMirrorTests
 ```
 
+Run it on Yggdrasil's `mcr.microsoft.com/dotnet/sdk:10.0` image (Ubuntu 24.04) only: that image owns the fixture's platform
+families and `device-bounds-lavapipe.txt`, and `CULTMATH_WRITE_GLSL=1` fails on any other OS. Re-record the bounds there in
+the same revision (`WRITE_BOUNDS=1`, `tools/device/run-lavapipe.sh`).
+
 `GlslMirrorTests.CommittedGlslEqualsLowering` fails on any difference between
 either committed file and the lowering of the committed HLSL. These
 transformations, in order, are the complete list:
@@ -519,11 +525,12 @@ running `float4(unit normal toward the owner, distance)` and the radical plane o
 the distance built from the offset `owner - p` and the weight difference `(w1 - w2)(w1 + w2)` so it does not
 cancel for close sites seen from far; the cell boundary distance is the least over every site except the owner
 (the fold's nearest), and a site coincident with the owner has no plane. The step trusts the caller's owner: a
-query outside the owner's cell reports distance 0 with that plane's normal, not an error. `power_border(p, sites)` is that loop.
+query outside the owner's cell reports distance 0 with that plane's normal, not an error. `power_border(p, sites)` is that loop;
+the shader's `cultmath_power_border(p, sites, count)` is the same loop over a by-value array (see "Sites in a shader" below).
 Cell spans refuse a non-finite query, site position or weight, and more than 2^24 sites (indices are floats).
 `power_cells` and
 `multiplicative_cells` are that loop over a `ReadOnlySpan<float4>` and nothing else; a shader caller writes the
-same loop over its own buffer. Every site of an explicit span is visited, so no window and no weight-ratio range
+same loop over its own array. Every site of an explicit span is visited, so no window and no weight-ratio range
 apply. `CultSiteCells` holds the two score fields and the two site indices (floats, -1 for none).
 
 `gabriel_margin(a, b, other)` is `(|other - (a + b) / 2| - r) / r` with `r = |a - b| / 2`: zero on the diameter
@@ -557,8 +564,21 @@ The accepted range is boost 0 to `LatticeMaxBoost` (4, a weight ratio of 10:1),
 and smoothing up to `LatticeMaxSmoothing` (1); outside it the function throws `ArgumentException`. `LatticeMaxRing`
 (37) is the proven greatest ring at the range edge. Measured over 24,000 points on orbiting bodies (six bodies,
 sigma ratio 6:1, the ruled look and the range edge), the greatest ring visited has median 3, 99th percentile 7 and
-maximum 8 (49, 225 and 289 cells); `RingsStayWellInsideTheCap` asserts these. The function is C# only; the shader
-twins are the next cut.
+maximum 8 (49, 225 and 289 cells); `RingsStayWellInsideTheCap` asserts these.
+
+### Sites in a shader
+
+A shader function cannot take a span, so `cultmath_power_border(p, sites, count)`, `cultmath_lattice_cell_distance(...)`
+and `cultmath_weighted_lattice_cells(p, time, bodies, count, ...)` take `float4 sites[CULTMATH_MAX_SITES]` by value and the
+count in use, with `count` in `[0, CULTMATH_MAX_SITES]`. `CULTMATH_MAX_SITES` is 128 unless the consumer defines it before
+including the library (`#ifndef`): 128 covers every Aetheria zone within GLSL ES 3.00's 224 guaranteed fragment uniform
+vectors, and loops run to `count`, so the capacity costs uniform space, not iterations. A `StructuredBuffer` caller copies
+into a local array first; the library takes no resource, accessor macro or uniform of its own. The preconditions the C#
+functions throw for are the caller's in a shader (finite arguments, `cellSize > 0`, the stated ranges, `p` within 2^23
+cells). The ring pass is bounded `k <= 37` and exits as C# does; the box pass recomputes each distance instead of caching
+75 x 75 of them, which gives the same values. The C# mirror compiles the array as `T[]`, and
+`HlslSourceCompatibilityTests.SiteArrayMirrorsMatchCSharp` compares the three functions through the span twins in
+`SiteArrays` (reflection cannot pass a `ReadOnlySpan`); `CULTMATH_MAX_SITES` is a shader-only capacity with no C# twin.
 
 ## Intervals
 
diff --git a/packages/cultmath/shaders/CultMath.hlsl b/packages/cultmath/shaders/CultMath.hlsl
index 94bec900..480074f2 100644
--- a/packages/cultmath/shaders/CultMath.hlsl
+++ b/packages/cultmath/shaders/CultMath.hlsl
@@ -600,14 +600,12 @@ CultCellular cultmath_cellular(float3 p)
     return result;
 }
 
-// Sites: a site is float4(position.xyz, weight). A span is a loop over a per-site step, because a shader
-// function cannot take a span in the mirror (design.md, "Sites"). The consumer's loop, over its own buffer:
+// Sites: a site is float4(position.xyz, weight). A shader function cannot take a span (design.md, "Sites"), so a span is a
+// fixed-capacity array and a count (cultmath_power_border, below), or a loop over a per-site step:
 //   CultSiteCells cells = cultmath_site_cells_empty();
 //   for (int i = 0; i < count; i++)
 //       cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
-// The exact power cell border is a second loop over the buffer, skipping the owner cells.nearestSite:
-//   float4 border = float4(0.0, 0.0, 0.0, 1.0e30); int owner = (int)cells.nearestSite;
-//   for (int k = 0; k < count; k++) if (k != owner) border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+// The exact power cell border is cultmath_power_border, the second loop over the sites that skips the owner cells.nearestSite.
 // The step trusts the owner: a p outside the owner's cell reports distance 0 with that plane's normal, not an error.
 // Statement for statement with math.Sites.cs (power_score, multiplicative_score, site_cells_*, gabriel_margin).
 struct CultSiteCells
@@ -688,21 +686,8 @@ float cultmath_gabriel_margin(float3 a, float3 b, float3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
-// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
-// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
-//   float2 q = p / cellSize; int2 c0 = (int2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
-//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
-//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
-//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
-//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
-//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
-//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
-//       reach = k; }
-//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
-//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
-// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
-// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
-// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement; cultmath_weighted_lattice_cells,
+// after them, is the whole function.
 float3 cultmath_lattice_site(float2 cell, float time, float drift)
 {
     int3 h = cultmath_pcg3d(int3((int)cell.x, (int)cell.y, 0));
@@ -734,6 +719,90 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
     return min(next, f1 + smoothing);
 }
 
+// Sites by value: a shader function cannot take a span, so these take float4 sites[CULTMATH_MAX_SITES] and the count in use, with
+// count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
+// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
+// cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the
+// box pass recomputes each distance instead of caching it (a 75 x 75 private array is not a shader option), with the same values.
+#ifndef CULTMATH_MAX_SITES
+#define CULTMATH_MAX_SITES 128
+#endif
+
+float4 cultmath_power_border(float3 p, float4 sites[CULTMATH_MAX_SITES], int count)
+{
+    CultSiteCells cells = cultmath_site_cells_empty();
+    for (int i = 0; i < count; i++)
+        cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
+    float4 border = float4(0.0, 0.0, 0.0, 1.0e30);
+    int owner = (int)cells.nearestSite;
+    if (owner < 0)
+        return border;
+    for (int k = 0; k < count; k++)
+        if (k != owner)
+            border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+    return border;
+}
+
+float cultmath_lattice_cell_distance(float2 q, float2 cell, float time, float drift, float4 bodies[CULTMATH_MAX_SITES], int count,
+    float cellSize, float boost, float falloff, float2 normal, float stretch)
+{
+    float3 site = cultmath_lattice_site(cell, time, drift);
+    float border = cultmath_power_border(float3((cell + 0.5) * cellSize, 0.0), bodies, count).w;
+    return cultmath_lattice_distance(q, site.xy, cultmath_lattice_weight(site.z, border, boost, falloff), normal, stretch);
+}
+
+float4 cultmath_weighted_lattice_cells(float2 p, float time, float4 bodies[CULTMATH_MAX_SITES], int count, float cellSize, float drift,
+    float boost, float falloff, float smoothing, float2 stretchNormal, float stretch)
+{
+    float scale = max(abs(stretchNormal.x), abs(stretchNormal.y));
+    float2 normal = float2(1.0, 0.0);
+    if (scale > 0.0)
+    {
+        normal = stretchNormal / scale;
+        normal = normal / length(normal);
+    }
+    float2 q = p / cellSize;
+    float2 origin = floor(q);
+    int cx0 = (int)origin.x;
+    int cz0 = (int)origin.y;
+    float f1 = 1.0e30;
+    float f2 = 1.0e30;
+    int reach = 0;
+    for (int k = 0; k <= 37; k++)
+    {
+        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+            break;
+        for (int dz = -k; dz <= k; dz++)
+        {
+            int step = dz == -k || dz == k || k == 0 ? 1 : 2 * k;
+            for (int dx = -k; dx <= k; dx += step)
+            {
+                float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+                if (d < f1) { f2 = f1; f1 = d; }
+                else if (d < f2) f2 = d;
+            }
+        }
+        reach = k;
+    }
+    float m = f1 + smoothing;
+    float best = 1.0e30;
+    float second = 1.0e30;
+    int winDx = 0;
+    int winDz = 0;
+    for (int dz = -reach; dz <= reach; dz++)
+        for (int dx = -reach; dx <= reach; dx++)
+        {
+            float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+            if (d < best) { second = best; best = d; winDx = dx; winDz = dz; }
+            else if (d < second) second = d;
+            m = cultmath_lattice_smooth_step(m, d, f1, smoothing);
+        }
+    int4 id = cultmath_pcg4d(int4(cx0 + winDx, cz0 + winDz, 0, 0));
+    return float4(best, second, m, (float)((uint)id.w >> 8) * (1.0 / 16777216.0));
+}
+
 float2 cultmath_segment_closest(float2 point_value, float2 start, float2 end)
 {
     float2 segment = end - start;
diff --git a/packages/cultmath/src/CultMath/math.Lattice.cs b/packages/cultmath/src/CultMath/math.Lattice.cs
index 42ae963b..a3c6ddba 100644
--- a/packages/cultmath/src/CultMath/math.Lattice.cs
+++ b/packages/cultmath/src/CultMath/math.Lattice.cs
@@ -200,7 +200,7 @@ public static partial class math
         return new float4(best, second, m, cellular_unit(id.w));
     }
 
-    private static float lattice_cell_distance(
+    internal static float lattice_cell_distance(
         float2 q, float2 cell, float time, float drift, ReadOnlySpan<float4> bodies, float cellSize, float boost, float falloff,
         float2 normal, float stretch)
     {
diff --git a/packages/cultmath/tests/CultMath.Tests/GlslLowering.cs b/packages/cultmath/tests/CultMath.Tests/GlslLowering.cs
index 5684535e..9af009f3 100644
--- a/packages/cultmath/tests/CultMath.Tests/GlslLowering.cs
+++ b/packages/cultmath/tests/CultMath.Tests/GlslLowering.cs
@@ -70,8 +70,9 @@ internal static class GlslLowering
         var source = hlsl.ReplaceLineEndings("\n");
 
         // 2. Include guards are dropped, and so are the functions taking Texture2D/SamplerState, exactly
-        //    as the C# mirror drops them; the host shader samples its own textures.
-        source = Regex.Replace(source, @"(?m)^[ \t]*#(ifndef|define|endif)\b.*$", string.Empty);
+        //    as the C# mirror drops them; the host shader samples its own textures. The capacity macro
+        //    (#ifndef CULTMATH_MAX_SITES ... #endif) stays: GLSL has the preprocessor, and a consumer overrides it.
+        source = HlslSourceCompatibilityTests.DropGuards(source, (name, value) => $"#ifndef {name}\n#define {name} {value}\n#endif");
         source = Regex.Replace(source, @"(?ms)^\w+ \w+\([^)]*\b(Texture2D|SamplerState)\b[^)]*\)\s*\{.*?^\}[ \t]*$", string.Empty);
 
         // 3. Type names: floatN, intN, uintN and boolN become vecN, ivecN, uvecN and bvecN, and float3x3
diff --git a/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.cs b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.cs
index 3ee41606..c2b604f6 100644
--- a/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.cs
@@ -22,7 +22,11 @@ public sealed partial class GlslMirrorTests
 
     public GlslMirrorTests(ITestOutputHelper output) => this.output = output;
 
-    private static bool Write => Environment.GetEnvironmentVariable("CULTMATH_WRITE_GLSL") == "1";
+    // The fixture is written by Yggdrasil's mcr.microsoft.com/dotnet/sdk:10.0 image (Ubuntu 24.04) only: its platform families record
+    // that platform's libm, so a write from another OS would move them.
+    private static bool Write => Environment.GetEnvironmentVariable("CULTMATH_WRITE_GLSL") == "1"
+        ? OperatingSystem.IsLinux() ? true : throw new InvalidOperationException("CULTMATH_WRITE_GLSL=1 writes glsl-parity.json, whose platform families belong to Yggdrasil's Ubuntu image (mcr.microsoft.com/dotnet/sdk:10.0): regenerate it there.")
+        : false;
 
     private static string Root => HlslSourceCompatibilityTests.FindCultMathRoot();
 
@@ -497,6 +501,14 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
             return (int)scalars.Dequeue();
         if (type == typeof(uint))
             return scalars.Dequeue();
+        if (type.IsArray)
+        {
+            var array = Array.CreateInstance(type.GetElementType()!, SiteArrays.Capacity);
+            for (var i = 0; i < array.Length; i++)
+                array.SetValue(FromScalars(type.GetElementType()!, scalars), i);
+            return array;
+        }
+
         var value = Activator.CreateInstance(type)!;
         foreach (var field in type.GetFields().Where(f => !f.IsStatic))
             field.SetValue(value, FromScalars(field.FieldType, scalars));
@@ -872,14 +884,26 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
         }),
         // The smooth step: d exactly at f1 + 2 smoothing one in four (the equal branch), near it one in four, the
         // smoothing near 0 and at 1, m anywhere up to f1 + smoothing.
+        // One draw in four is the cap point: m = f1 + smoothing exactly and d = f1 + smoothing (1 + U(0.3, 0.9)) with smoothing in
+        // [0.5, 1], where next exceeds f1 + smoothing and the min clamps; a step that returns next reads another function there.
         new Family("float cultmath_lattice_smooth_step(float, float, float, float)", "ulp-bounded", r =>
         {
+            if (r.Next(4) == 0)
+            {
+                var cappedSmoothing = Uniform(r, 0.5f, 1.0f);
+                var cappedF1 = Uniform(r, 0.0f, 10.0f);
+                return new object[] { cappedF1 + cappedSmoothing, cappedF1 + cappedSmoothing * (1.0f + Uniform(r, 0.3f, 0.9f)), cappedF1, cappedSmoothing };
+            }
+
             var smoothing = r.Next(5) switch { 0 => 1.0f, 1 => Uniform(r, 1.0e-3f, 1.0e-2f), _ => Uniform(r, 0.01f, 1.0f) };
             var f1 = Uniform(r, 0.0f, 10.0f);
             var edge = f1 + 2.0f * smoothing;
             var d = r.Next(4) switch { 0 => edge, 1 => edge * Uniform(r, 0.99f, 1.01f), _ => Uniform(r, f1, edge + 1.0f) };
             return new object[] { Uniform(r, f1, f1 + smoothing), d, f1, smoothing };
         }),
+        // The site-array functions: a fixed-capacity array and a count, killed on the device (the lattice at rings up to 17).
+        new Family($"vec4 cultmath_power_border(vec3, vec4[{SiteArrays.Capacity}], int)", "ulp-bounded", SiteArrays.PowerBorderArguments),
+        new Family($"vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[{SiteArrays.Capacity}], int, float, float, float, float, float, vec2, float)", "ulp-bounded", SiteArrays.LatticeArguments),
     }).ToArray();
 
     // A point of magnitude m, m log-uniform in [lo, hi]: one component at +-m, the other two uniform in [-m, m],
@@ -988,6 +1012,7 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
         ["vec4"] = typeof(float4), ["ivec3"] = typeof(int3), ["ivec4"] = typeof(int4),
         ["SpanPath"] = typeof(SpanPath), ["SpanStage"] = typeof(SpanStage),
         ["CultSiteCells"] = typeof(CultSiteCells),
+        [$"vec4[{SiteArrays.Capacity}]"] = typeof(float4[]),
     };
 
     // The C# math method a GLSL signature names: cultmath_ dropped, parameter types mapped.
@@ -996,6 +1021,7 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
         var match = Regex.Match(glsl, @"^\w+ cultmath_(\w+)\(([^)]*)\)$");
         var types = match.Groups[2].Value.Split(", ").Select(t => GlslTypes[t]).ToArray();
         return typeof(math).GetMethod(match.Groups[1].Value, BindingFlags.Public | BindingFlags.Static, null, types, null)
+            ?? typeof(SiteArrays).GetMethod(match.Groups[1].Value, BindingFlags.NonPublic | BindingFlags.Static, null, types, null)
             ?? throw new InvalidOperationException("no C# math counterpart for " + glsl);
     }
 
@@ -1011,6 +1037,8 @@ static int4 clamp(int4 x, int4 a, int4 b) { if (a.x > b.x || a.y > b.y || a.z >
     // the same read as GLSL's columns.
     private static IEnumerable<object> Scalars(object value) => value is float or int or uint
         ? new[] { value }
+        : value is Array array
+        ? array.Cast<object>().SelectMany(Scalars)
         : value is float3x3 matrix
         ? new object[] { matrix._m00, matrix._m01, matrix._m02, matrix._m10, matrix._m11, matrix._m12, matrix._m20, matrix._m21, matrix._m22 }
         : value.GetType().GetFields().Where(f => !f.IsStatic).SelectMany(f => Scalars(f.GetValue(value)!));
diff --git a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
index 3cb5070a..cfcd2c66 100644
--- a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
@@ -70,7 +70,7 @@ public sealed class HlslSourceCompatibilityTests
         shader.GetMethod(name, BindingFlags.Instance | BindingFlags.NonPublic, null, parameters, null);
 
     // Shader constants with no C# twin of the same name (empty when every constant has one).
-    private static readonly string[] ConstantsWithoutTwin = Array.Empty<string>();
+    private static readonly string[] ConstantsWithoutTwin = { "CULTMATH_MAX_SITES" };
 
     /// <summary>
     /// Every static const of the compiled HLSL mirror (a static literal CULTMATH_* field, whatever its access) is the
@@ -85,7 +85,7 @@ public sealed class HlslSourceCompatibilityTests
         Assert.True(assembly is not null, string.Join(Environment.NewLine, errors));
         var shader = assembly!.GetType("CultMathHlsl.HlslShader")!;
         var constants = shader.GetFields(BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Static)
-            .Where(f => f.IsLiteral && f.Name.StartsWith("CULTMATH_", StringComparison.Ordinal))
+            .Where(f => f.IsLiteral && f.FieldType == typeof(float) && f.Name.StartsWith("CULTMATH_", StringComparison.Ordinal))
             .ToArray();
         Assert.True(constants.Length >= 10, $"only {constants.Length} shader constants were found by reflection");
         foreach (var constant in constants)
@@ -183,7 +183,7 @@ public sealed class HlslSourceCompatibilityTests
 
         var mismatches = new List<string>();
         var compared = new HashSet<string>();
-        foreach (var mirror in shaderType.GetMethods(BindingFlags.Instance | BindingFlags.NonPublic).Where(m => m.Name.StartsWith("cultmath_")))
+        foreach (var mirror in shaderType.GetMethods(BindingFlags.Instance | BindingFlags.NonPublic).Where(m => m.Name.StartsWith("cultmath_") && !m.GetParameters().Any(p => p.ParameterType.IsArray)))
         {
             var types = mirror.GetParameters().Select(p => p.ParameterType).ToArray();
             var counterpart = Twin(shaderType, mirror.Name["cultmath_".Length..], types);
@@ -204,7 +204,65 @@ public sealed class HlslSourceCompatibilityTests
         }
 
         Assert.True(mismatches.Count == 0, $"{mismatches.Count} mismatches:{Environment.NewLine}{string.Join(Environment.NewLine, mismatches.Take(12))}");
-        Assert.Equal(140, compared.Count);
+        // The three site-array functions are compared by SiteArrayMirrorsMatchCSharp, which draws their counts and arrays.
+        Assert.Equal(137, compared.Count);
+    }
+
+    /// <summary>
+    /// The shader functions that take a site array and a count are bit-equal to C#'s span functions on the same
+    /// arguments: at least 64 compared cases each, counts 0 to the capacity with filler after the count (a loop bound that
+    /// ignores the count reads it), the lattice at rings up to 17. A case C# refuses is skipped and counted.
+    /// </summary>
+    [Fact]
+    public void SiteArrayMirrorsMatchCSharp()
+    {
+        var (assembly, errors) = CompileShaderMirror();
+        Assert.True(assembly is not null, string.Join(Environment.NewLine, errors));
+        var shaderType = assembly!.GetType("CultMathHlsl.HlslShader")!;
+        var shader = Activator.CreateInstance(shaderType);
+        Assert.Equal(17, SiteArrays.FarPoints[0].Ring);
+        Assert.All(SiteArrays.FarPoints, far => Assert.InRange(far.Ring, 8, LatticeMaxRing));
+
+        var draws = new (string Name, Func<System.Random, object[]> Draw)[]
+        {
+            ("power_border", SiteArrays.PowerBorderArguments),
+            ("lattice_cell_distance", SiteArrays.LatticeCellDistanceArguments),
+            ("weighted_lattice_cells", SiteArrays.LatticeArguments),
+        };
+        foreach (var (name, draw) in draws)
+        {
+            var mirror = shaderType.GetMethod("cultmath_" + name, BindingFlags.Instance | BindingFlags.NonPublic)!;
+            var twin = typeof(SiteArrays).GetMethod(name, BindingFlags.Static | BindingFlags.NonPublic)!;
+            Assert.Equal(twin.GetParameters().Select(p => p.ParameterType), mirror.GetParameters().Select(p => p.ParameterType));
+            var random = new System.Random(0x517E);
+            int compared = 0, refused = 0;
+            for (var i = 0; i < 160; i++)
+            {
+                var args = draw(random);
+                object expected;
+                try { expected = twin.Invoke(null, args)!; }
+                catch (TargetInvocationException e) when (e.InnerException is ArgumentException) { refused++; continue; }
+                var actual = Values(mirror.Invoke(shader, args)!);
+                Assert.True(BitwiseEqual(Values(expected), actual),
+                    $"{name} case {i}: C# {string.Join(" ", Values(expected).Select(v => v.Value))}, mirror {string.Join(" ", actual.Select(v => v.Value))}");
+                compared++;
+            }
+
+            Assert.True(compared >= 64, $"{name} compared only {compared} cases ({refused} refused)");
+        }
+    }
+
+    /// <summary>A consumer defines CULTMATH_MAX_SITES before including the library; the mirror compiles with the capacity changed.</summary>
+    [Fact]
+    public void TheSiteCapacityIsOverridable()
+    {
+        var (assembly, errors) = CompileShaderMirror(defines: new Dictionary<string, int> { ["CULTMATH_MAX_SITES"] = 4 });
+        Assert.True(assembly is not null, string.Join(Environment.NewLine, errors));
+        var shaderType = assembly!.GetType("CultMathHlsl.HlslShader")!;
+        Assert.Equal(4, (int)shaderType.GetField("CULTMATH_MAX_SITES", BindingFlags.Public | BindingFlags.NonPublic | BindingFlags.Static)!.GetRawConstantValue()!);
+        var sites = new[] { new float4(0, 0, 0, 1), new float4(10, 0, 0, 1), new float4(0, 10, 0, 2), new float4(-10, 0, 0, 1) };
+        var border = (float4)shaderType.GetMethod("cultmath_power_border", BindingFlags.Instance | BindingFlags.NonPublic)!.Invoke(Activator.CreateInstance(shaderType), new object[] { new float3(1, 1, 0), sites, 4 })!;
+        Assert.Equal(power_border(new float3(1, 1, 0), sites), border);
     }
 
     /// <summary>
@@ -682,14 +740,23 @@ public sealed class HlslSourceCompatibilityTests
                 : string.Empty);
     }
 
+    /// <summary>
+    /// The text without its include-guard lines. A capacity macro (<c>#ifndef X</c>, <c>#define X n</c>, <c>#endif</c>, a
+    /// consumer-overridable default) is not a guard: <paramref name="capacity"/> gives the text it becomes, from its name and value.
+    /// </summary>
+    internal static string DropGuards(string source, Func<string, string, string> capacity) =>
+        Regex.Replace(source, @"(?m)^#ifndef (CULTMATH_MAX_\w+)\r?\n#define \1 (\d+)\r?\n#endif[ \t]*$|^[ \t]*#(ifndef|define|endif)\b.*$",
+            match => match.Groups[1].Success ? capacity(match.Groups[1].Value, match.Groups[2].Value) : string.Empty);
+
     /// <summary>
     /// The documented HLSL-to-C# transformations, and nothing else. <paramref name="members"/> is C# source a
     /// test supplies, placed first in the class body: it is not a transformation of the HLSL.
     /// </summary>
-    internal static string TransformHlslToCSharp(string hlsl, string members = "")
+    internal static string TransformHlslToCSharp(string hlsl, string members = "", IReadOnlyDictionary<string, int>? defines = null)
     {
-        // 1. Include guards (#ifndef/#define/#endif) are dropped; C# has no textual include.
-        var source = Regex.Replace(hlsl, @"(?m)^\s*#(ifndef|define|endif)\b.*$", string.Empty);
+        // 1. Include guards (#ifndef/#define/#endif) are dropped; C# has no textual include. A capacity macro
+        //    (#ifndef X, #define X n, #endif) becomes `const int X = n;`, or the value a test defines for X.
+        var source = DropGuards(hlsl, (name, value) => $"const int {name} = {(defines is not null && defines.TryGetValue(name, out var defined) ? defined : value)};");
 
         // 2. Functions taking Texture2D/SamplerState resources are dropped; GPU resources have
         //    no CultMath analog.
@@ -708,14 +775,17 @@ public sealed class HlslSourceCompatibilityTests
         source = Regex.Replace(source, @"(?ms)(struct\s+\w+\s*\{)(.*?)(\};)", m =>
             m.Groups[1].Value + Regex.Replace(m.Groups[2].Value, @"(?m)^(\s*)(\w+\s+\w+;)", "$1public $2") + m.Groups[3].Value);
 
-        // 6. The file body is wrapped in a class; C# has no free functions.
+        // 6. An array parameter `T name[N]` becomes `T[] name`; the mirror takes the array whole and the count beside it.
+        source = Regex.Replace(source, @"\b(\w+) (\w+)\[CULTMATH_MAX_\w+\]", "$1[] $2");
+
+        // 7. The file body is wrapped in a class; C# has no free functions.
         return "using CultMath;\nusing static CultMath.math;\nnamespace CultMathHlsl;\npublic class HlslShader\n{\n" + members + source + "\n}\n";
     }
 
-    internal static (Assembly? Assembly, IReadOnlyList<string> Errors) CompileShaderMirror(string members = "")
+    internal static (Assembly? Assembly, IReadOnlyList<string> Errors) CompileShaderMirror(string members = "", IReadOnlyDictionary<string, int>? defines = null)
     {
         var hlsl = ReadShaderSource(FindCultMathRoot());
-        var tree = CSharpSyntaxTree.ParseText(TransformHlslToCSharp(hlsl, members));
+        var tree = CSharpSyntaxTree.ParseText(TransformHlslToCSharp(hlsl, members, defines));
         var references = ((string)AppContext.GetData("TRUSTED_PLATFORM_ASSEMBLIES")!)
             .Split(Path.PathSeparator)
             .Append(typeof(math).Assembly.Location)
diff --git a/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs b/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
index 741c3d58..22de49c8 100644
--- a/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
@@ -9,19 +9,19 @@ namespace CultMath.Tests;
 /// </summary>
 public sealed class LatticeCellsTests
 {
-    private const float Cell = 260.0f;
-    private const float Falloff = 120.0f;
-    private const float Drift = 0.7f;
-    private static readonly float2 Normal = new(0.6f, 0.8f);
+    internal const float Cell = 260.0f;
+    internal const float Falloff = 120.0f;
+    internal const float Drift = 0.7f;
+    internal static readonly float2 Normal = new(0.6f, 0.8f);
 
-    private sealed record Look(float Boost, float Stretch, float Smoothing, float Falloff = LatticeCellsTests.Falloff);
+    internal sealed record Look(float Boost, float Stretch, float Smoothing, float Falloff = LatticeCellsTests.Falloff);
 
-    private static readonly Look[] Looks =
+    internal static readonly Look[] Looks =
     {
         new(1.6f, 1.0f, 0.35f), new(1.6f, 2.0f, 0.35f), new(LatticeMaxBoost, LatticeMaxStretch, LatticeMaxSmoothing), new(0.0f, 1.0f, 0.05f),
     };
 
-    private static float4[] Bodies(float t)
+    internal static float4[] Bodies(float t)
     {
         var bodies = new float4[6];
         for (var i = 0; i < bodies.Length; i++)
@@ -74,7 +74,7 @@ public sealed class LatticeCellsTests
     private static float4 Call(float2 p, float time, float4[] bodies, Look look, float2? normal = null) =>
         weighted_lattice_cells(p, time, bodies, Cell, Drift, look.Boost, look.Falloff, look.Smoothing, normal ?? Normal, look.Stretch);
 
-    private static float2 RandomPoint(System.Random r) =>
+    internal static float2 RandomPoint(System.Random r) =>
         new((r.NextSingle() * 2.0f - 1.0f) * 1500.0f, (r.NextSingle() * 2.0f - 1.0f) * 1500.0f);
 
     [Fact]
@@ -97,9 +97,9 @@ public sealed class LatticeCellsTests
             }
     }
 
-    private delegate bool Stop(int k, float f1, float f2, Look look);
+    internal delegate bool Stop(int k, float f1, float f2, Look look);
 
-    private static readonly (string name, Stop stop)[] Rules =
+    internal static readonly (string name, Stop stop)[] Rules =
     {
         ("correct", (k, f1, f2, l) => k > 1 && 0.5f * (k - 1) >= max(f2, f1 + 2.0f * l.Smoothing)),
         ("cutoff F1 + k", (k, f1, f2, l) => k > 1 && 0.5f * (k - 1) >= max(f2, f1 + l.Smoothing)),
@@ -109,7 +109,7 @@ public sealed class LatticeCellsTests
     };
 
     // The radius of the box a search with the given exit rule visits (rings 0 to k - 1 when it stops before ring k).
-    private static int Radius(float2 p, float time, float4[] bodies, Look look, Stop stop,
+    internal static int Radius(float2 p, float time, float4[] bodies, Look look, Stop stop,
         Dictionary<(int, int), float> weights)
     {
         var q = p / Cell;
diff --git a/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
new file mode 100644
index 00000000..b299cc67
--- /dev/null
+++ b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
@@ -0,0 +1,129 @@
+using CultMath;
+using static CultMath.math;
+
+namespace CultMath.Tests;
+
+/// <summary>
+/// The shader's site-array functions as C# twins. A shader function cannot take a span, so
+/// <c>cultmath_power_border</c>, <c>cultmath_lattice_cell_distance</c> and <c>cultmath_weighted_lattice_cells</c> take
+/// <c>float4 sites[CULTMATH_MAX_SITES]</c> and a count; reflection cannot pass a <see cref="ReadOnlySpan{T}"/>, so each
+/// twin takes the array and the count and calls the span function on <c>sites[..count]</c>. This table is the one
+/// place that maps them, read by the mirror test and by the GLSL fixture. The draws are the cases both run.
+/// </summary>
+internal static class SiteArrays
+{
+    /// <summary>The shader's default CULTMATH_MAX_SITES; the device families spell their array with it.</summary>
+    internal const int Capacity = 128;
+
+    internal static float4 power_border(float3 p, float4[] sites, int count) => math.power_border(p, sites.AsSpan(0, count));
+
+    internal static float lattice_cell_distance(
+        float2 q, float2 cell, float time, float drift, float4[] bodies, int count, float cellSize, float boost, float falloff,
+        float2 normal, float stretch) =>
+        math.lattice_cell_distance(q, cell, time, drift, bodies.AsSpan(0, count), cellSize, boost, falloff, normal, stretch);
+
+    internal static float4 weighted_lattice_cells(
+        float2 p, float time, float4[] bodies, int count, float cellSize, float drift, float boost, float falloff,
+        float smoothing, float2 stretchNormal, float stretch) =>
+        math.weighted_lattice_cells(p, time, bodies.AsSpan(0, count), cellSize, drift, boost, falloff, smoothing, stretchNormal, stretch);
+
+    // The array the shader receives: the sites, then filler a loop running past the count would read. The filler is
+    // finite and large, so a loop bound that ignores the count changes the result.
+    private static float4[] Padded(IReadOnlyList<float4> sites)
+    {
+        var array = new float4[Capacity];
+        for (var i = 0; i < Capacity; i++)
+            array[i] = i < sites.Count ? sites[i] : new float4(40.0f * (i + 1), -30.0f * (i + 1), 7.0f, 90.0f + i);
+        return array;
+    }
+
+    private static float Uniform(System.Random r, float lo, float hi) => lo + (hi - lo) * r.NextSingle();
+
+    // Counts 0, 1, 6, 16 and the capacity are drawn often; the rest of [0, Capacity] fills between.
+    private static int Count(System.Random r) => r.Next(3) == 0 ? r.Next(Capacity + 1) : new[] { 0, 1, 6, 16, Capacity }[r.Next(5)];
+
+    // Bodies on slow orbits (float4(position.xy, 0, sigma)), spread over the plane the lattice cells cover.
+    private static float4[] Orbit(System.Random r, int count, float time)
+    {
+        var bodies = new List<float4>();
+        for (var i = 0; i < count; i++)
+        {
+            var angle = 0.001f * (i + 1) * time + i;
+            var radius = 100.0f + 2400.0f * r.NextSingle();
+            bodies.Add(new float4(radius * MathF.Cos(angle), radius * MathF.Sin(angle), 0.0f, Uniform(r, 20.0f, 300.0f)));
+        }
+
+        return Padded(bodies);
+    }
+
+    internal static object[] PowerBorderArguments(System.Random r)
+    {
+        var count = Count(r);
+        var sites = new List<float4>();
+        for (var i = 0; i < count; i++)
+            sites.Add(new float4(Uniform(r, -1500.0f, 1500.0f), Uniform(r, -1500.0f, 1500.0f), Uniform(r, -200.0f, 200.0f), Uniform(r, 10.0f, 300.0f)));
+        return new object[] { new float3(Uniform(r, -1500.0f, 1500.0f), Uniform(r, -1500.0f, 1500.0f), Uniform(r, -200.0f, 200.0f)), Padded(sites), count };
+    }
+
+    internal static object[] LatticeCellDistanceArguments(System.Random r)
+    {
+        var angle = Uniform(r, 0.0f, 6.2831855f);
+        var look = LatticeCellsTests.Looks[r.Next(LatticeCellsTests.Looks.Length)];
+        var cell = new float2(r.Next(-300, 300), r.Next(-300, 300));
+        var count = Count(r);
+        return new object[]
+        {
+            new float2(Uniform(r, -1500.0f, 1500.0f), Uniform(r, -1500.0f, 1500.0f)) / LatticeCellsTests.Cell, cell, Uniform(r, 0.0f, 200.0f), LatticeCellsTests.Drift,
+            Orbit(r, count, Uniform(r, 0.0f, 200.0f)), count, LatticeCellsTests.Cell, look.Boost, look.Falloff, new float2(MathF.Cos(angle), MathF.Sin(angle)), look.Stretch,
+        };
+    }
+
+    // The unit-less normals the function normalises itself: ordinary, 3-4-5, tiny, huge, and zero (stretch 1 only).
+    private static readonly float2[] Normals = { LatticeCellsTests.Normal, new(3.0f, 4.0f), new(3.0e-30f, -4.0e-30f), new(1.0e30f, 2.0e30f), new(0.0f, 0.0f) };
+
+    /// <summary>
+    /// Points whose ring search runs to ring 8 or past it under the widest look (boost, stretch and smoothing at their
+    /// maxima, falloff so wide that every cell is boosted), found once by the radius the exit rule visits, and the
+    /// ring-17 point of LatticeCellsTests.TheCapIsReachedAndMatchesTheFullBox first. Each is (p, time).
+    /// </summary>
+    internal static readonly IReadOnlyList<(float2 P, float Time, int Ring)> FarPoints = FindFarPoints();
+
+    internal static readonly LatticeCellsTests.Look WidestLook = new(LatticeMaxBoost, LatticeMaxStretch, LatticeMaxSmoothing, 1.0e6f);
+
+    private static List<(float2, float, int)> FindFarPoints()
+    {
+        var found = new List<(float2, float, int)>();
+        var cap = (new float2(1446.7345f, -680.7637f), 97.69269f);
+        found.Add((cap.Item1, cap.Item2, LatticeCellsTests.Radius(cap.Item1, cap.Item2, LatticeCellsTests.Bodies(cap.Item2), WidestLook, LatticeCellsTests.Rules[0].stop, new Dictionary<(int, int), float>())));
+        var r = new System.Random(0x1A77);
+        while (found.Count < 12)
+        {
+            var p = LatticeCellsTests.RandomPoint(r);
+            var time = 13.0f * r.Next(20);
+            var ring = LatticeCellsTests.Radius(p, time, LatticeCellsTests.Bodies(time), WidestLook, LatticeCellsTests.Rules[0].stop, new Dictionary<(int, int), float>());
+            if (ring >= 8)
+                found.Add((p, time, ring));
+        }
+
+        return found;
+    }
+
+    internal static object[] LatticeArguments(System.Random r)
+    {
+        if (r.Next(3) == 0)
+        {
+            var far = FarPoints[r.Next(FarPoints.Count)];
+            return Lattice(far.P, far.Time, Padded(LatticeCellsTests.Bodies(far.Time)), 6, WidestLook, LatticeCellsTests.Normal);
+        }
+
+        var time = 13.0f * r.Next(20);
+        var normal = Normals[r.Next(Normals.Length)];
+        var look = normal.x == 0.0f ? LatticeCellsTests.Looks[0] : LatticeCellsTests.Looks[r.Next(LatticeCellsTests.Looks.Length)];
+        var count = Count(r);
+        return Lattice(LatticeCellsTests.RandomPoint(r), time, Orbit(r, count, time), count, look, normal);
+    }
+
+    private static object[] Lattice(float2 p, float time, float4[] bodies, int count, LatticeCellsTests.Look look, float2 normal) =>
+        new object[] { p, time, bodies, count, LatticeCellsTests.Cell, LatticeCellsTests.Drift,
+            look.Boost, look.Falloff, look.Smoothing, normal, look.Stretch };
+}
diff --git a/packages/cultmath/tools/device/gen.py b/packages/cultmath/tools/device/gen.py
index a2ae8104..b408a4ea 100644
--- a/packages/cultmath/tools/device/gen.py
+++ b/packages/cultmath/tools/device/gen.py
@@ -16,6 +16,7 @@ import sys
 HLSL_VEC = re.compile(r'(float|int|uint)([234])$')
 GLSL_VEC = re.compile(r'(i|u|)vec([234])$')
 KIND = {'float': 'f', 'int': 'i', 'uint': 'u'}
+ARRAY = re.compile(r'(\w+)\[(\d+)\]$')  # an array leaf, vec4[128]: N elements of one leaf type, N x its words
 
 
 def structs(root):
@@ -79,6 +80,19 @@ def body(sig, n, win, wout, defs, glsl):
     ret, name, params = m.group(1), m.group(2), [p.strip() for p in m.group(3).split(',') if p.strip()]
     lines, offset, args = [], 0, []
     for j, p in enumerate(params):
+        array = ARRAY.match(p)
+        if array:
+            elem, size = array.group(1), int(array.group(2))
+            words = leaves(elem, defs)
+            lines.append('    %s a%d[%d];' % (elem if glsl else hlsl_type(elem), j, size))
+            lines.append('    for (uint e = 0u; e < %du; e++) {' % size)
+            for k, leaf in enumerate(words):
+                word = ('In.a[b + %du + e * %du]' if glsl else 'In[b + %du + e * %du]') % (offset + k, len(words))
+                lines.append('        a%d[e]%s = %s;' % (j, access(leaf, glsl), read(leaf[1], glsl, word)))
+            lines.append('    }')
+            offset += size * len(words)
+            args.append('a%d' % j)
+            continue
         ptype = p if glsl else hlsl_type(p)
         lines.append('    %s a%d;' % (ptype, j))
         for leaf in leaves(p, defs):
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
index 94bec900..480074f2 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
+++ b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
@@ -600,14 +600,12 @@ CultCellular cultmath_cellular(float3 p)
     return result;
 }
 
-// Sites: a site is float4(position.xyz, weight). A span is a loop over a per-site step, because a shader
-// function cannot take a span in the mirror (design.md, "Sites"). The consumer's loop, over its own buffer:
+// Sites: a site is float4(position.xyz, weight). A shader function cannot take a span (design.md, "Sites"), so a span is a
+// fixed-capacity array and a count (cultmath_power_border, below), or a loop over a per-site step:
 //   CultSiteCells cells = cultmath_site_cells_empty();
 //   for (int i = 0; i < count; i++)
 //       cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
-// The exact power cell border is a second loop over the buffer, skipping the owner cells.nearestSite:
-//   float4 border = float4(0.0, 0.0, 0.0, 1.0e30); int owner = (int)cells.nearestSite;
-//   for (int k = 0; k < count; k++) if (k != owner) border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+// The exact power cell border is cultmath_power_border, the second loop over the sites that skips the owner cells.nearestSite.
 // The step trusts the owner: a p outside the owner's cell reports distance 0 with that plane's normal, not an error.
 // Statement for statement with math.Sites.cs (power_score, multiplicative_score, site_cells_*, gabriel_margin).
 struct CultSiteCells
@@ -688,21 +686,8 @@ float cultmath_gabriel_margin(float3 a, float3 b, float3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
-// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
-// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
-//   float2 q = p / cellSize; int2 c0 = (int2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
-//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
-//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
-//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
-//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
-//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
-//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
-//       reach = k; }
-//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
-//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
-// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
-// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
-// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement; cultmath_weighted_lattice_cells,
+// after them, is the whole function.
 float3 cultmath_lattice_site(float2 cell, float time, float drift)
 {
     int3 h = cultmath_pcg3d(int3((int)cell.x, (int)cell.y, 0));
@@ -734,6 +719,90 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
     return min(next, f1 + smoothing);
 }
 
+// Sites by value: a shader function cannot take a span, so these take float4 sites[CULTMATH_MAX_SITES] and the count in use, with
+// count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
+// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
+// cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the
+// box pass recomputes each distance instead of caching it (a 75 x 75 private array is not a shader option), with the same values.
+#ifndef CULTMATH_MAX_SITES
+#define CULTMATH_MAX_SITES 128
+#endif
+
+float4 cultmath_power_border(float3 p, float4 sites[CULTMATH_MAX_SITES], int count)
+{
+    CultSiteCells cells = cultmath_site_cells_empty();
+    for (int i = 0; i < count; i++)
+        cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
+    float4 border = float4(0.0, 0.0, 0.0, 1.0e30);
+    int owner = (int)cells.nearestSite;
+    if (owner < 0)
+        return border;
+    for (int k = 0; k < count; k++)
+        if (k != owner)
+            border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+    return border;
+}
+
+float cultmath_lattice_cell_distance(float2 q, float2 cell, float time, float drift, float4 bodies[CULTMATH_MAX_SITES], int count,
+    float cellSize, float boost, float falloff, float2 normal, float stretch)
+{
+    float3 site = cultmath_lattice_site(cell, time, drift);
+    float border = cultmath_power_border(float3((cell + 0.5) * cellSize, 0.0), bodies, count).w;
+    return cultmath_lattice_distance(q, site.xy, cultmath_lattice_weight(site.z, border, boost, falloff), normal, stretch);
+}
+
+float4 cultmath_weighted_lattice_cells(float2 p, float time, float4 bodies[CULTMATH_MAX_SITES], int count, float cellSize, float drift,
+    float boost, float falloff, float smoothing, float2 stretchNormal, float stretch)
+{
+    float scale = max(abs(stretchNormal.x), abs(stretchNormal.y));
+    float2 normal = float2(1.0, 0.0);
+    if (scale > 0.0)
+    {
+        normal = stretchNormal / scale;
+        normal = normal / length(normal);
+    }
+    float2 q = p / cellSize;
+    float2 origin = floor(q);
+    int cx0 = (int)origin.x;
+    int cz0 = (int)origin.y;
+    float f1 = 1.0e30;
+    float f2 = 1.0e30;
+    int reach = 0;
+    for (int k = 0; k <= 37; k++)
+    {
+        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+            break;
+        for (int dz = -k; dz <= k; dz++)
+        {
+            int step = dz == -k || dz == k || k == 0 ? 1 : 2 * k;
+            for (int dx = -k; dx <= k; dx += step)
+            {
+                float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+                if (d < f1) { f2 = f1; f1 = d; }
+                else if (d < f2) f2 = d;
+            }
+        }
+        reach = k;
+    }
+    float m = f1 + smoothing;
+    float best = 1.0e30;
+    float second = 1.0e30;
+    int winDx = 0;
+    int winDz = 0;
+    for (int dz = -reach; dz <= reach; dz++)
+        for (int dx = -reach; dx <= reach; dx++)
+        {
+            float d = cultmath_lattice_cell_distance(q, float2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+            if (d < best) { second = best; best = d; winDx = dx; winDz = dz; }
+            else if (d < second) second = d;
+            m = cultmath_lattice_smooth_step(m, d, f1, smoothing);
+        }
+    int4 id = cultmath_pcg4d(int4(cx0 + winDx, cz0 + winDz, 0, 0));
+    return float4(best, second, m, (float)((uint)id.w >> 8) * (1.0 / 16777216.0));
+}
+
 float2 cultmath_segment_closest(float2 point_value, float2 start, float2 end)
 {
     float2 segment = end - start;

From 8f74369dee2bb713023253c20f7c170e4bf88f35 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:18:56 +0200
Subject: [PATCH 04/21] SiteArrays: WidestLook initialises before FarPoints

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/tests/CultMath.Tests/SiteArrays.cs | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
index b299cc67..cc3a4bf8 100644
--- a/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
+++ b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
@@ -81,6 +81,8 @@ internal static class SiteArrays
     // The unit-less normals the function normalises itself: ordinary, 3-4-5, tiny, huge, and zero (stretch 1 only).
     private static readonly float2[] Normals = { LatticeCellsTests.Normal, new(3.0f, 4.0f), new(3.0e-30f, -4.0e-30f), new(1.0e30f, 2.0e30f), new(0.0f, 0.0f) };
 
+    internal static readonly LatticeCellsTests.Look WidestLook = new(LatticeMaxBoost, LatticeMaxStretch, LatticeMaxSmoothing, 1.0e6f);
+
     /// <summary>
     /// Points whose ring search runs to ring 8 or past it under the widest look (boost, stretch and smoothing at their
     /// maxima, falloff so wide that every cell is boosted), found once by the radius the exit rule visits, and the
@@ -88,8 +90,6 @@ internal static class SiteArrays
     /// </summary>
     internal static readonly IReadOnlyList<(float2 P, float Time, int Ring)> FarPoints = FindFarPoints();
 
-    internal static readonly LatticeCellsTests.Look WidestLook = new(LatticeMaxBoost, LatticeMaxStretch, LatticeMaxSmoothing, 1.0e6f);
-
     private static List<(float2, float, int)> FindFarPoints()
     {
         var found = new List<(float2, float, int)>();

From 96d83c7f1bb3b596ebaf5d487a7eb4ec9144b133 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:21:45 +0200
Subject: [PATCH 05/21] CultMath: regenerate CultMath.glsl and glsl-parity.json
 on Yggdrasil (Ubuntu) for the site-array families

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/shaders/CultMath.glsl       |  109 +-
 .../HlslSourceCompatibilityTests.cs           |    2 +-
 .../CultMath.Tests/fixtures/glsl-parity.json  | 1210 ++++++++++++-----
 3 files changed, 957 insertions(+), 364 deletions(-)

diff --git a/packages/cultmath/shaders/CultMath.glsl b/packages/cultmath/shaders/CultMath.glsl
index 41f40279..32318111 100644
--- a/packages/cultmath/shaders/CultMath.glsl
+++ b/packages/cultmath/shaders/CultMath.glsl
@@ -600,14 +600,12 @@ CultCellular cultmath_cellular(vec3 p)
     return result;
 }
 
-// Sites: a site is vec4(position.xyz, weight). A span is a loop over a per-site step, because a shader
-// function cannot take a span in the mirror (design.md, "Sites"). The consumer's loop, over its own buffer:
+// Sites: a site is vec4(position.xyz, weight). A shader function cannot take a span (design.md, "Sites"), so a span is a
+// fixed-capacity array and a count (cultmath_power_border, below), or a loop over a per-site step:
 //   CultSiteCells cells = cultmath_site_cells_empty();
 //   for (int i = 0; i < count; i++)
 //       cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
-// The exact power cell border is a second loop over the buffer, skipping the owner cells.nearestSite:
-//   vec4 border = vec4(0.0, 0.0, 0.0, 1.0e30); int owner = int(cells.nearestSite);
-//   for (int k = 0; k < count; k++) if (k != owner) border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+// The exact power cell border is cultmath_power_border, the second loop over the sites that skips the owner cells.nearestSite.
 // The step trusts the owner: a p outside the owner's cell reports distance 0 with that plane's normal, not an error.
 // Statement for statement with math.Sites.cs (power_score, multiplicative_score, site_cells_*, gabriel_margin).
 struct CultSiteCells
@@ -688,21 +686,8 @@ float cultmath_gabriel_margin(vec3 a, vec3 b, vec3 other)
     return (cultmath_distance(other, (a + b) * 0.5) - r) / r;
 }
 
-// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement. A shader function cannot take a
-// span (design.md, "Sites"), so weighted_lattice_cells is the consumer's loop over its own body buffer, in two passes:
-//   vec2 q = p / cellSize; ivec2 c0 = (ivec2)floor(q); float f1 = 1.0e30, f2 = 1.0e30; int reach = 0;
-//   for (int k = 0; ; k++) {   // ring pass: Chebyshev rings 0, 1, 2, ... around c0, exact exit
-//       if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing)) break;   // k never reaches 38 in the accepted range
-//       for each cell on ring k: d = cultmath_lattice_distance(q, cultmath_lattice_site(cell, time, drift).xy, w, normal, stretch),
-//           w = cultmath_lattice_weight(site.z, border, boost, falloff), border = the .w of cultmath_power_border_step
-//           folded over the bodies (owner = the nearest body of the cell centre (cell + 0.5) * cellSize, z = 0);
-//           if (d < f1) { f2 = f1; f1 = d; } else if (d < f2) f2 = d;   store d for the box pass
-//       reach = k; }
-//   float m = f1 + smoothing;   // box pass: every stored cell, rows dz = -reach..reach, then dx = -reach..reach
-//   for each (dz, dx): m = cultmath_lattice_smooth_step(m, d, f1, smoothing);   // strict < for the winning id (earlier cell wins ties)
-// The preconditions the C# function throws for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
-// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. The normal is normalised as C# does: divide by its
-// largest component, then by its length (a zero normal means (1, 0) and needs stretch == 1). The ring bound is 37.
+// Weighted lattice cells: the four per-cell steps of math.Lattice.cs, statement for statement; cultmath_weighted_lattice_cells,
+// after them, is the whole function.
 vec3 cultmath_lattice_site(vec2 cell, float time, float drift)
 {
     ivec3 h = cultmath_pcg3d(ivec3(int(cell.x), int(cell.y), 0));
@@ -734,6 +719,90 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
     return min(next, f1 + smoothing);
 }
 
+// Sites by value: a shader function cannot take a span, so these take vec4 sites[CULTMATH_MAX_SITES] and the count in use, with
+// count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
+// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
+// falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
+// cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the
+// box pass recomputes each distance instead of caching it (a 75 x 75 private array is not a shader option), with the same values.
+#ifndef CULTMATH_MAX_SITES
+#define CULTMATH_MAX_SITES 128
+#endif
+
+vec4 cultmath_power_border(vec3 p, vec4 sites[CULTMATH_MAX_SITES], int count)
+{
+    CultSiteCells cells = cultmath_site_cells_empty();
+    for (int i = 0; i < count; i++)
+        cells = cultmath_site_cells_insert(cells, cultmath_power_score(p, sites[i]), i);
+    vec4 border = vec4(0.0, 0.0, 0.0, 1.0e30);
+    int owner = int(cells.nearestSite);
+    if (owner < 0)
+        return border;
+    for (int k = 0; k < count; k++)
+        if (k != owner)
+            border = cultmath_power_border_step(p, sites[owner], sites[k], border);
+    return border;
+}
+
+float cultmath_lattice_cell_distance(vec2 q, vec2 cell, float time, float drift, vec4 bodies[CULTMATH_MAX_SITES], int count,
+    float cellSize, float boost, float falloff, vec2 normal, float stretch)
+{
+    vec3 site = cultmath_lattice_site(cell, time, drift);
+    float border = cultmath_power_border(vec3((cell + 0.5) * cellSize, 0.0), bodies, count).w;
+    return cultmath_lattice_distance(q, site.xy, cultmath_lattice_weight(site.z, border, boost, falloff), normal, stretch);
+}
+
+vec4 cultmath_weighted_lattice_cells(vec2 p, float time, vec4 bodies[CULTMATH_MAX_SITES], int count, float cellSize, float drift,
+    float boost, float falloff, float smoothing, vec2 stretchNormal, float stretch)
+{
+    float scale = max(abs(stretchNormal.x), abs(stretchNormal.y));
+    vec2 normal = vec2(1.0, 0.0);
+    if (scale > 0.0)
+    {
+        normal = stretchNormal / scale;
+        normal = normal / length(normal);
+    }
+    vec2 q = p / cellSize;
+    vec2 origin = floor(q);
+    int cx0 = int(origin.x);
+    int cz0 = int(origin.y);
+    float f1 = 1.0e30;
+    float f2 = 1.0e30;
+    int reach = 0;
+    for (int k = 0; k <= 37; k++)
+    {
+        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+            break;
+        for (int dz = -k; dz <= k; dz++)
+        {
+            int step = dz == -k || dz == k || k == 0 ? 1 : 2 * k;
+            for (int dx = -k; dx <= k; dx += step)
+            {
+                float d = cultmath_lattice_cell_distance(q, vec2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+                if (d < f1) { f2 = f1; f1 = d; }
+                else if (d < f2) f2 = d;
+            }
+        }
+        reach = k;
+    }
+    float m = f1 + smoothing;
+    float best = 1.0e30;
+    float second = 1.0e30;
+    int winDx = 0;
+    int winDz = 0;
+    for (int dz = -reach; dz <= reach; dz++)
+        for (int dx = -reach; dx <= reach; dx++)
+        {
+            float d = cultmath_lattice_cell_distance(q, vec2(cx0 + dx, cz0 + dz), time, drift, bodies, count, cellSize, boost, falloff, normal, stretch);
+            if (d < best) { second = best; best = d; winDx = dx; winDz = dz; }
+            else if (d < second) second = d;
+            m = cultmath_lattice_smooth_step(m, d, f1, smoothing);
+        }
+    ivec4 id = cultmath_pcg4d(ivec4(cx0 + winDx, cz0 + winDz, 0, 0));
+    return vec4(best, second, m, float(uint(id.w) >> 8) * (1.0 / 16777216.0));
+}
+
 vec2 cultmath_segment_closest(vec2 point_value, vec2 start, vec2 end)
 {
     vec2 segment = end - start;
diff --git a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
index cfcd2c66..41770546 100644
--- a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
@@ -205,7 +205,7 @@ public sealed class HlslSourceCompatibilityTests
 
         Assert.True(mismatches.Count == 0, $"{mismatches.Count} mismatches:{Environment.NewLine}{string.Join(Environment.NewLine, mismatches.Take(12))}");
         // The three site-array functions are compared by SiteArrayMirrorsMatchCSharp, which draws their counts and arrays.
-        Assert.Equal(137, compared.Count);
+        Assert.Equal(140, compared.Count);
     }
 
     /// <summary>
diff --git a/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json b/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
index acfd786d..8f1fa987 100644
--- a/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
+++ b/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
@@ -2728,7 +2728,7 @@
         "4022181e 40221be2 4181cf61 41847273 -> c1605ede c15b17ca",
         "bfc63914 bfc5886c 41558bdf 4159d691 -> c1729db4 c16e3cec",
         "41719da7 4171a109 c19eb92a c19eaade -> 420bbcd9 420bc4d7",
-        "40f2e763 4120d76e bf81ca38 401a0c2c -> 40a5e14d 413110b5",
+        "40f2e763 4120d76e bf81ca39 401a0c2c -> 40a5e14d 413110b5",
         "403ecb1f 40410e41 c101976e c0ed526d -> 41265bfe 4131dafe",
         "3f2502e7 3f250e19 4180e4db 4180e97d -> c17782cc c17778d4",
         "c1749928 c1741414 c185bb15 c1846fd3 -> 3fa233f0 3fbb10b0",
@@ -5056,7 +5056,7 @@
         "c12a1ca9 c129e60f c026bfa8 41214e89 -> c026bfa8 c026bfa8",
         "41646d2a 41989373 c11d417d 40befd8d -> 40befd8d 40befd8d",
         "416e3268 4181ee24 bf563220 417bb26e -> 416e3268 417bb26e",
-        "c0c50d72 be9aa860 bfb35300 41894251 -> bfb35300 be9aa860",
+        "c0c50d72 be9aa858 bfb35300 41894251 -> bfb35300 be9aa858",
         "410fef0b 4114c15d c164037e 3fd35dff -> 3fd35dff 3fd35dff",
         "4106ccec 4113b120 c0832e1c 41374ad7 -> 4106ccec 4113b120",
         "c1122227 c1121dd1 c0976074 41bfcfbd -> c0976074 c0976074",
@@ -6820,7 +6820,7 @@
     {
       "glsl": "vec2 cultmath_iv_exp(vec2)",
       "tolerance": "ulp-bounded, platform exp",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "41202b2a 4120314e -> 46ade79e 46ae2a6b",
         "c0d1a016 bfb9db96 -> 3abb4cbc 3e6fb77f",
@@ -6917,7 +6917,7 @@
         "40c71490 4165a95c -> 43fbab24 49d1201c",
         "3fc1015d 3fc19163 -> 40908b7c 40912e7d",
         "c17ee168 c151c9c2 -> 34019755 3607a61b",
-        "c0c3c1de 3fa3ddfa -> 3b10736b 40663bd3",
+        "c0c3c1df 3fa3ddfc -> 3b107367 40663bd7",
         "c17826ef c17819e9 -> 34455621 3445f704",
         "c159be3f c159b8bf -> 35a50371 35a53c36",
         "c0020079 bffad0ae -> 3e0650d0 3e104fe8",
@@ -7083,11 +7083,11 @@
     {
       "glsl": "CultPhasor cultmath_phacelle(vec3, vec3, float, float)",
       "tolerance": "ulp-bounded, platform exp, sin, cos; across platforms |diff| <= 2^-20 max(|v|, 1); on a device |diff| <= 2^-18 max(|v|, 1)",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
-        "c01d8630 41b2cd8c 41ea274c bfa19894 40aeb6ce 40918978 3e9be843 3f000000 -> bf74d9fb 3fb71956 bf35fe4e 3f21280a c01277e2 403b5fe7 40464bbd bd5b4455",
+        "c01d8630 41b2cd8c 41ea274c bfa19894 40aeb6ce 40918978 3e9be843 3f000000 -> bf74d9fb 3fb71956 bf35fe4e 3f21280a c01277e2 403b5fe4 40464bbd bd5b4455",
         "c2234cf7 4237b112 419ae0c0 c0acbcd4 bf60f9a0 bfeb2b08 3ebf0a10 3f000000 -> c0d0048f 3f228da3 bfc85f60 3edaf41b c0171c80 be137f8c be1c92a3 bf5747bf",
-        "41cc0920 42390a28 c1c4714d 4095ff5a 40ae1422 40138f40 3ea0019d 3f000000 -> c0626854 c06c83d4 bfb294eb be676f09 bfcf7e6e 3d2e2183 c0200a4a 3f167e2e",
+        "41cc0920 42390a28 c1c4714d 4095ff5a 40ae1422 40138f40 3ea0019d 3f000000 -> c0626854 c06c83d4 bfb294eb be676f09 bfcf7e6e 3d2e218b c0200a4a 3f167e2f",
         "42370b68 c2438846 c1e6efa5 c03373ff 402d665c 4013a940 3e578396 3f000000 -> 3d678d11 3e4c172f beeb5835 be30e395 3f0a6332 3ede254b bee8e250 3eae4126",
         "c08f5578 411586a8 42413a4c c019de34 3fc5c70c bf08ccf0 3f5a6e2e 3f000000 -> 401e1cfd bfc4bac6 bf58739f 3f279e2b bcc6aac3 3f322772 3edf42e6 3df7608b",
         "c11d6390 41b27d04 c17248a0 402cdca8 c0bf8bd5 c0829639 3effad62 3f000000 -> bf03c0db 3ff17078 3f87ac38 3f75d4e0 3fe2b4b6 c0cfb86d c0697330 3e8ede55",
@@ -7097,16 +7097,16 @@
         "c156c260 41a86c28 41c868c0 4064de10 40964edc 3e7448e0 3eb4f280 3f000000 -> bf8c32e0 bffb8ca7 3d8b13de 3e438cc7 3f323542 3f99dc06 40017862 3e874112",
         "c1d068b3 42225982 c205c8f0 40ad9ff8 3ec5dd80 40707e58 3f0ce75b 3f000000 -> c0349e81 3f3fc530 bfaf1dbc bf18915a c08caaaa 3eac5ccd c005c769 3e9225e7",
         "c1e59fe1 41a04784 4208ac42 c0920956 bee7b4a0 c07134a5 3ea378b1 3f000000 -> bf3feef3 bdb8ba0b bfa29638 be587b15 3f3930d2 3ef203a1 3fff1a53 bdbfd9a5",
-        "42389eb6 4106e060 c15fbf54 3ffd6f00 3e9e6f60 bffcb888 3f3075cd 3f000000 -> 3f332fdb 3c8560ce bfe1216d 3c2f34bf 3bf5488d 393690af bc9a1676 bf7ffc41",
+        "42389eb6 4106e060 c15fbf54 3ffd6f00 3e9e6f60 bffcb888 3f3075cd 3f000000 -> 3f332fdc 3c8560b8 bfe1216d 3c2f34ca 3bf5488d 393690af bc9a1676 bf7ffc41",
         "c20f4cf6 c1dfe857 bed31800 40717ea8 c0a6b312 408b5396 3d29b33a 3f000000 -> bfdb8d4f 403490e4 3fb46b68 3e471378 bd600a14 bfbec46f 3fc2be3f 3eaf81a2",
         "c224ee6a 41d06018 414aa3f8 4024db50 40215b48 40036b94 3f657d0a 3f000000 -> bff064ec 3f7da25d 3e056ae2 be8ac707 bf782c47 bed3745c c00c9402 bcacdb39",
         "41b4d2e4 c1d569b9 4242f024 bf523eb0 c0933fbf 40b37860 3effacc8 3f000000 -> be71736c bd8a544e 3c17c22f 3f7aa6b3 bf04a68a c05faf26 40b9af6e bd872883",
         "421867b6 c1aa947d c21c327e 402c6040 409cb72c c00c5822 3ecef6a5 3f000000 -> 402c1659 40ac0e18 c01c7aba 3e2e0e0e 3eed75dd 3f6d6a7b bed7ec61 bf7c4657",
         "c2158204 c12f6f30 c212cbea bfce6068 c0725f30 3ffc14b0 3dc82c17 3f000000 -> bf1395df bf305c8f bd010deb 3c80722f 3faded2e bcab6bdf 3e04aa20 3d81745f",
-        "41949b58 4187ba84 c210eb56 becef150 40aceb96 3ddc8e80 3e004e03 3f000000 -> 3f1c001d bfbfd00c 3f9c703f bf46ef9f 3ee1430a c015c256 3facb8b2 3e843e47",
+        "41949b58 4187ba84 c210eb56 becef150 40aceb96 3ddc8e80 3e004e03 3f000000 -> 3f1c001d bfbfd00c 3f9c703f bf46ef9f 3ee14306 c015c255 3facb8b2 3e843e47",
         "422ff3b8 c1e3f97a c117efcc 4041ae24 3e35fc40 bf6d0858 3e712c37 3f000000 -> bfdb3c1a bdd2c0db 3f47d294 bf103816 bf957c53 bd8fb3dc 3f083fd8 3f5382c9",
-        "c16e4c30 c14b7fe0 c1d54085 bf8b652c bfca9a04 c06e21c5 3e857f24 3f000000 -> bfff4d45 3eda6cb0 c0881cdc 3e7adfa2 3e134e33 bfc64ff6 bec024d0 bf36ee7d",
-        "422d5612 c135cecc c224002b c0836a40 3f0bfd30 3fd2bf48 3f762107 3f000000 -> 4058e898 bf411a77 bfb68041 3eaab859 bf996e7b 3e8897c4 3f0117dc 3f715983",
+        "c16e4c30 c14b7fe0 c1d54085 bf8b652c bfca9a04 c06e21c5 3e857f24 3f000000 -> bfff4d45 3eda6caf c0881cdc 3e7adfa2 3e134e36 bfc64ff6 bec024d1 bf36ee7d",
+        "422d5612 c135cecc c224002b c0836a40 3f0bfd30 3fd2bf48 3f762107 3f000000 -> 4058e898 bf411a76 bfb68041 3eaab85a bf996e7b 3e8897c4 3f0117dc 3f715983",
         "c14fd0a4 bf22c600 c17192b0 3e9dd3c0 c0bd4f62 40656694 3d24f368 3f000000 -> beff75fe c0d75ce4 4082d09b bcb4fe19 3c34a7be 3e184c99 bdb90498 bf7ff000",
         "40cb6f18 420bdb7a 423a18e2 c0802b55 beff9dc0 bfc16eb0 3f70ee13 3f000000 -> c05a7f35 3bd810da bfa0cad2 bf57161c 40a94183 bc275f6f 3ff91c8a bf0ad490",
         "c22b4d81 41a392ec 423ce770 bfa3e2d8 409774fa c07e6f32 3f46714c 3f000000 -> bfdd6fa6 c021e2ac 3f2cb532 bdb4ffec 3f462d16 3f9d4611 bd304b02 3e837570",
@@ -7122,10 +7122,10 @@
         "422bfc72 408d09e0 41cadff4 bf949404 40b76420 c05932ce 3e0260c0 3f000000 -> 3e1ad712 c0700bfc 4035036a 3e345710 3f873541 3ed84397 bf4514a3 3f2c6e39",
         "4182b7f0 3fdb3500 423dfe3e 3ff98528 409c70a4 3db12680 3f38a282 3f000000 -> 3ef90c71 3fbabdde 3cffa967 3f70ef28 3fad5f13 4081ff52 3db1f9b3 bead0d2a",
         "413263c8 bfec49e0 c18d8a1c 3fa248b0 40ac1f40 3e0a2c00 3d090b54 3f000000 -> bca80779 3e97874d be698984 3ed80cf6 400f1075 3fccdce2 c02c14f7 be947a34",
-        "c14cd5dc 421796b6 c13e9a50 bd739d00 c06779b4 40898cda 3f76729b 3f000000 -> 3dc4e9ea 401d4ac1 c064800e 3d4e6b1f 3f0e7a22 bd288139 bf8f7aa8 3f1baa65",
+        "c14cd5dc 421796b6 c13e9a50 bd739d00 c06779b4 40898cda 3f76729b 3f000000 -> 3dc4e9ea 401d4ac1 c064800e 3d4e6b1f 3f0e7a24 bd288139 bf8f7aa8 3f1baa65",
         "418f6740 41f235c8 4215cd42 bf2b2258 bf9e2864 40096424 3f5f39ba 3f000000 -> be5562ac bf1d54e0 3f6bf72d 3f43aa38 be7cebc0 bf3a7b3d 3f8bd79c bf25145c",
         "c21af350 c244d836 c1fd5079 c04d5704 c084cb9b c054b65e 3f7c2c02 3f000000 -> c02a3303 c06ce177 c052a8f5 bf0fe3fb 3fe753f7 4020fab9 400f290a bf53bc0b",
-        "c1d91797 422434ca 412c86c4 c0a6a1ff be700520 4051c5d0 3ca2ec6d 3f000000 -> bf1cff90 bda671eb 3ec4b468 3f7e5aae c0ac3c44 bf369952 4057cba2 bde7da32",
+        "c1d91797 422434ca 412c86c4 c0a6a1ff be700520 4051c5d0 3ca2ec6d 3f000000 -> bf1cff92 bda671ee 3ec4b46b 3f7e5aae c0ac3c44 bf369954 4057cba2 bde7da35",
         "c1d68924 4105a85c c232ef2e 3f547b60 bfb8f8a0 3f50ae20 3f0ed843 3f000000 -> bd6ae04d 3e01e51e 3e889d50 bf7356a6 3e33b352 bec6c2fc bf510b30 be9f06e2",
         "41841508 c14ba5c8 42234a50 405641f4 bfd89908 c080c7a1 3f7bf0dc 3f000000 -> bf3b659f 3ec0b685 3f5fef14 bca2d5fe beed41b9 3fcc95eb bf9ffd2c 3e6bca16",
         "41ab7d88 c21fcf04 c1e179b7 3dfeaf00 407c2510 40861d2c 3eff6bda 3f000000 -> bdcb6bb1 c05d2a17 c0889194 3f1af01f 3d9aa858 402825d1 404fa971 3f4bca27",
@@ -7162,22 +7162,22 @@
         "c18fbce6 c22dfc75 c0efbca8 4081c10a 3fa33a00 409759ea 3f67ef0c 3f000000 -> bf3f410e bf22565c 3f2ec5e2 bed5b35d c03d3bcc bf0b39ee c00f3505 be7c1db3",
         "41dc9120 41066fb4 41e51bb4 c0af079e be40fae0 3f9102d0 3a428d58 3f000000 -> 40858dd5 3fa1c560 bfc5d334 bf01413a 40289b75 3f7b7b03 c01d7e4a 3f0b485f",
         "c204b70a c0e6eab0 405ddf70 3f8cb560 3fe47360 c009a082 3f05139d 3f000000 -> 3e0506c1 3fb50296 3ddaf7a8 3da04aa2 be4289ee 402cda41 c04a45dd befee595",
-        "41e775b8 41a13c24 3fff4440 c0ab4f3c c0af6a4b 4062f6d0 3ef83151 3f000000 -> c0938b46 c0791d1e 402f4bb1 3ddd00cd bf001f39 bed8524b 3e983873 bf7e814d",
+        "41e775b8 41a13c24 3fff4440 c0ab4f3c c0af6a4b 4062f6d0 3ef83151 3f000000 -> c0938b46 c0791d1e 402f4bb1 3ddd00cd bf001f3a bed8524c 3e983873 bf7e814d",
         "c1990bdd c22aca80 4143abc0 3f8f0ed4 409ecb36 40bd3d24 3f3f7d18 3f000000 -> 3e7c42ad c02acd31 c02ad591 3f5df0f6 bedb68e4 40948f0c 40949653 3eff2bcd",
         "c21697f6 c21a8540 422f2efa c0b2df61 40bc3f6a c09e501f 3cdafb54 3f000000 -> 404b0750 bff7ce6c 3f54574b 3e692377 bf9b078c 3f74d3af 3f4e90a2 3e170af8",
         "416a6ce0 c1a40321 c224844e c0875f12 3e02c380 c050400e 3f717c7e 3f000000 -> 3f5bfafd bf578513 3e09b82a bf210791 40546be4 bf3e6ade 3fbb2d42 3ea4603f",
-        "bf13d980 c187a568 c224fbf8 4017ddcc c08280e5 c0b7b521 3f07efce 3f000000 -> c035c7e9 4046f7b3 408de22d 3eda80e7 3f27ddb6 c0458a5f c0085163 3f5ebdad",
+        "bf13d980 c187a568 c224fbf8 4017ddcc c08280e5 c0b7b521 3f07efce 3f000000 -> c035c7e9 4046f7b2 408de22d 3eda80e7 3f27ddb6 c0458a5f c0085163 3f5ebdad",
         "c15a6a20 42220e4a 41e33738 3f41c650 c09a217d bf71f350 3eef1ccb 3f000000 -> bf9232a6 bfd661c0 bf881c2f 3dd9ae5b bf511ebb bf7d8751 be02f9d2 be208642",
         "3f8ccd80 c2065d14 c09c9e60 3f596790 3f9c0e48 c03de55e 3d3713ad 3f000000 -> 3d8701f5 bf856906 3ee69b79 3f589fb3 bd5be9b1 3f9dc717 bed7dece 3ecce28f",
         "c194b02e 411abbf0 40b7bf58 3ff375b4 c04d0045 bda99740 3e123c80 3f000000 -> 3fe78ed8 c042110d 3ef8a224 bf318c2d c036b693 4081fc19 3f83136c beb7e53b",
         "c1158174 c0dc0c78 42229080 3ec7f980 3f4cdb70 3efea3f0 3f5080f0 3f000000 -> 3e73860e bd68f779 be9c8d3b 3e9f1250 3d9f3286 bc984bc7 bdccaeef bf7354c9",
         "41c2106c 405e6e80 421e2858 40429838 40b4f244 c0595821 3f429101 3f000000 -> bf08a4d0 3f0467fe bf3d3d16 3e670e91 3d3e3def 3ed61720 4047141f 3cdd6ce6",
-        "c1e92711 c20a6ca2 c038e830 409660e8 3fffb930 3f377180 3e0ac49b 3f000000 -> 3f558c3d 3f2b69c1 bf308c3e 3f2c6b1f 4072bb10 3fa110d8 3e8db4f1 bb867017",
+        "c1e92711 c20a6ca2 c038e830 409660e8 3fffb930 3f377180 3e0ac49b 3f000000 -> 3f558c3c 3f2b69c1 bf308c3f 3f2c6b1f 4072bb10 3fa110d8 3e8db4f1 bb866fe9",
         "c213a47c 415c3df4 40f57130 409d128a 40b6d2a8 409910e6 3e38682c 3f000000 -> c0609695 c0375c02 c08b0570 bf2306eb c0194810 c0870187 c045b923 3f3d16a2",
         "41bafc9c 4040c1d0 c2384dcc 40a3ff3e 3eaf13d0 bfabbbf0 3f74f97e 3f000000 -> c09ae81a 3fbb6006 3f9d6de1 be502d30 bf6b220d 3db0f756 bed9d3fa 3f554e4a",
         "c0270280 42170b1e c23bc9c1 3ec43160 4091d758 3fea50c4 3f44b72e 3f000000 -> bdf61ce9 406c7377 3fccac48 baeddb4e 3fab5485 3db1b1bb bfd68e22 bf307c0c",
-        "414ef014 40b21ee0 41fde9c0 3fc84534 c0b2469e c0255f52 3dd83a99 3f000000 -> 3d054e10 bd9dbe7f 3e93b33e beed3ddb 3f6c8450 407824b2 3d04c288 3e29c43d",
-        "c0b72308 c2257991 41d5836c 3f4c8c90 40a66b74 c0bd330a 3e8d23ff 3f000000 -> be960ca6 c0053936 3e27d970 be06b313 3fb1cec1 bfbd90a3 bf792711 3e1a0b35",
+        "414ef014 40b21ee0 41fde9c0 3fc84534 c0b2469e c0255f52 3dd83a99 3f000000 -> 3d054e09 bd9dbe7f 3e93b33e beed3ddb 3f6c8450 407824b2 3d04c278 3e29c43d",
+        "c0b72308 c2257991 41d5836c 3f4c8c90 40a66b74 c0bd330a 3e8d23ff 3f000000 -> be960ca6 c0053936 3e27d95c be06b313 3fb1cec1 bfbd90a3 bf792711 3e1a0b33",
         "41eadde8 c1883b50 41459bb8 3f8b2318 3fdb6564 3fce6960 3c10f1a3 3f000000 -> 3e2a07ce 3e976bc2 3e862015 3f7ac176 3f4ec396 3fb8224e 3fa31a12 be4e34e9",
         "c2462536 420e7624 42028568 bf2ff7c0 407c85d8 4068c688 3f3c1252 3f000000 -> bf98ace4 bffc1d44 c0491ccb 3e8a3a95 bd352040 3f921df4 3ef19767 3f2e5386",
         "c1b2ef80 c0be2610 c16083bc 405c2de8 409c59fe bfcc2428 3f006614 3f000000 -> 4005d507 404199d8 be0bb2fe be922beb c0366336 bf9059ee 3d024f4a bf452778",
@@ -7187,27 +7187,27 @@
         "419f9b74 42446f7a c1f9de1a c0611312 be625da0 bfc641f8 3e2a6f08 3f000000 -> 400ee70d be6ba7b2 3f33d83e bf22f77c 3febeadc be42856c 3f1473dc 3f456d95",
         "41692cc8 c114756c 41dfea20 c0b5ee8a 3fd75800 405283c0 3f362b17 3f000000 -> c05275e1 3edb82ec bf503b09 bf580669 40930788 bfe983dd c0866d83 be87e41f",
         "40e14890 c1783ecc 41705b40 c0b4e735 3f37f220 40275588 3f0f92a2 3f000000 -> c098015d 3f9e4ea3 403885e9 3ed705d2 c00cae84 3f12839b 3faac6ed bf685485",
-        "41061698 c05acd50 420b0b0c bf200920 c09137fb c0ab22d1 3f3a7a8c 3f000000 -> 3fac4705 405d74ef 3fc6b2e6 3f1823a6 bf7c495e c01de986 c09a3534 3efb88e0",
+        "41061698 c05acd50 420b0b0c bf200920 c09137fb c0ab22d1 3f3a7a8c 3f000000 -> 3fac4705 405d74ef 3fc6b2e6 3f1823a6 bf7c495e c01de987 c09a3534 3efb88e0",
         "c23a9414 c102ac08 409f2568 40956024 3fa5276c 4090b6aa 3ec3d45c 3f000000 -> c03644f7 bfc427a8 c068d345 bf289191 c033cf05 bf5aef0d c070d206 3ef8745d",
         "41d6939c c2239a52 41babdd8 c08d2c84 401c5920 c0902ebd 3f4c4e64 3f000000 -> 3f6d1340 bfbaa59f 3ebe7a7e 3d867d94 be1b76eb bf281843 be7ba74c 3df2a956",
         "42120dd8 4100f4b8 40dc7408 4038dc1c 409c595e 40b3fdaa 3f7a3d3f 3f000000 -> bfc33673 bffef515 c03c889a 3f270b90 4074c748 408c812d 4083588d 3e5d753d",
         "c22f20fc c1a7197a c1e98d2e bf002348 c0affda8 c0a7797e 3decf621 3f000000 -> 3eec79c4 4099377f 406dddce 3f115d84 bea3210e c0536376 c02416ab 3f52b98c",
         "4021c4e0 c17fe868 41cf392c bfd76bc8 c00cdb5a bf3e7170 3f1cb7da 3f000000 -> 3f2dcc2a 3f315cd7 3f09d94c bf19b99a bf9c3b88 3f07253b be70219d be6aa357",
-        "42438da6 c1d7df3c c2111ca0 c0b373da 40988b36 c0033d45 3f4d5bb2 3f000000 -> 4012b7e4 3f5c743d 3c8db62c bd901a7a 3f8ab549 3eb60a09 3fc49512 3dcd570a",
+        "42438da6 c1d7df3c c2111ca0 c0b373da 40988b36 c0033d45 3f4d5bb2 3f000000 -> 4012b7e4 3f5c743d 3c8db636 bd901a7a 3f8ab549 3eb60a09 3fc49512 3dcd570a",
         "c1c4eac1 4226b7e4 421e9d8a 4088d1b2 3f8f6600 4049ccb8 3f37fac1 3f000000 -> 3f3d1fc2 3ea8dcef 3f66ca8d 3f7646e5 40269fb6 3f94c5f7 404b5579 be8bc43e",
-        "421a15fe c1b106e9 41a5c304 c05b22b2 c09f207a 4040b7e4 3f78ac19 3f000000 -> 401a7e7d 406f51b9 bfdd05ae 3e8588b6 bef1ea6b 3e268e1e 3fbae05e 3f581092",
+        "421a15fe c1b106e9 41a5c304 c05b22b2 c09f207a 4040b7e4 3f78ac19 3f000000 -> 401a7e7d 406f51b9 bfdd05ac 3e8588b6 bef1ea6b 3e268e1e 3fbae05e 3f581092",
         "c2151e44 c17d52f0 c0ddba10 3f4a3c20 40706050 c0331dc2 3e78c661 3f000000 -> bf1b45e1 bf02a724 3e3068a7 3f672b51 40029c9f 4055188c bfdd893a 3e2cd55a",
         "41c8bf8c 423dc256 41da160c bfad9708 400f3ee4 c0713c62 3f60520b 3f000000 -> 3ff3a6ef c01c8623 bf00ae11 bf0f27cf 400efeae c01a4744 3ffdc24a bd54a470",
         "c16f4cd0 c0daa6f0 41a66bfc c0bc31d8 3fd67130 c0795b57 3f4eee55 3f000000 -> 409b4569 bf558889 4035a6c3 3f3c6aff c0a8cfb3 3f68277a c0457df7 3f2d4e1e",
         "c1491284 c196c840 41232e90 bf1eb940 c018bfb3 bf9e27f0 3f23db16 3f000000 -> 3f7f5350 3f838185 3fa294d9 bf1ee30d 3e5c5e79 bfa98a5b 3de4aca0 3d74a95a",
-        "c22f76a5 c23344eb c20df755 c04e9a64 400fabc0 3fd84688 3f5c96fd 3f000000 -> 40692189 bfd19f2f bf6b4309 3e8f7456 bf7755c7 bfdd4632 3f8d9965 3f6983dc",
+        "c22f76a5 c23344eb c20df755 c04e9a64 400fabc0 3fd84688 3f5c96fd 3f000000 -> 40692189 bfd19f2f bf6b430d 3e8f7457 bf7755c8 bfdd4632 3f8d9965 3f6983dc",
         "421b651e 41a53544 c05432c0 c09fa4f1 c0a80fc1 3f35f930 3f00bf43 3f000000 -> beea3767 3fefb99c 3f8ccf09 be2a0d41 3e1760b8 3f94851b 3ecd7130 bdd8dab9",
         "4230f58c c2166d7f c04463c0 409c3a0e 3f6c2460 40837d10 3f08e72a 3f000000 -> c01c16d9 bf07400b bfedb2cf bf27bdda c07c9495 3f425d8b c0178264 3ee3df2e",
         "420ad16a 4247ab84 c1ec31a2 bf25e630 3f684cf0 c081635a 3f40bc64 3f000000 -> bf6bb447 bf53d21f 3e84eba6 3e5d36f7 3f1bfc0a 3fd5cb13 bf978f7d be81d8e3",
         "c23bf09c 42037d1a c219000d 3e120000 408dfb1a 3f9e0710 3f30893b 3f000000 -> bfcc7bb5 bec50c07 3eaf8922 be220b89 3e3c8770 bf9a0da0 bfc9e61d bd94d272",
         "42290740 414c0974 c2099996 40bfc992 3f0a8170 c0ba676a 3eec84b5 3f000000 -> 40441441 bfd4da9c c018e65b 3f6ae859 408ffe01 3ff9e5cd c08eb6a7 bec5f101",
         "41b42100 c1cf0dad 422a4290 3f6d6070 3fb24cb8 c01572c8 3edd262d 3f000000 -> beef1c7a bdcfe77d 3f564c05 bf2dbd7f bedcf473 bdc01e16 3f46065a 3f3c0450",
-        "c1f9ed42 c212ee20 4084c5e8 402c3734 3f27c7a0 c097921e 3e5b707e 3f000000 -> bf819ee6 bea0058c 3fde894f 3ec594a4 3fd7a295 3e0c6677 c0415a62 3ead3500",
+        "c1f9ed42 c212ee20 4084c5e8 402c3734 3f27c7a0 c097921e 3e5b707e 3f000000 -> bf819ee5 bea0058d 3fde8951 3ec594a4 3fd7a293 3e0c6676 c0415a62 3ead3500",
         "c232f06f 4230217c 41e3fdc8 c09533bf be88b040 c096381b 3f5bbbfd 3f000000 -> c06f242b bf14e793 bfc4ff22 3ee388d2 c0392aab bf64486a c039cbce bf168559",
         "42171d88 c1710c80 40e79c20 c06c15b7 40af3d62 4070a218 3ca26c6a 3f000000 -> be6a59e7 3f6608c5 3ffb9f73 3dc14ee9 bf84c37f 3efa15df 400c80ba bd8df087",
         "beb7ed80 c195594f 4222f52c c0b3cba0 407bc8f4 c0a408c9 3df99e44 3f000000 -> c0a288e1 40708608 c09d54d0 3ed96bd0 c01878a2 3fe1a1a0 c013970b bf67c57f",
@@ -7229,12 +7229,12 @@
         "c1ad57b7 3fdc6ee0 41f355d0 40927334 3fa73d28 403e3220 3eb6eff5 3f000000 -> bf6d0f7f 3e4f7034 c0833b58 be18dcc9 bfb9ada4 3eb4ace0 bf8ea70f 3f198fad",
         "423ebd88 c22076d2 c1e6cab8 3fe13dc0 c0311946 40bfdb84 3ea78895 3f000000 -> 3f0821df c0431559 40e07c7b 3e483e55 3dd92881 bf1b9935 3fb30cd9 bf7b0ebe",
         "c15483a4 41e2edb8 4220c264 3f47a178 c087a5c5 c020d313 3cb89c14 3f000000 -> c000b46a 3ed9bd91 3f8b13c6 bef25c20 bfa8218e 4034d6d6 40147392 3e9c6f34",
-        "42199716 c1f5d9f0 c1d0e49e 402b9848 bfd62764 c0238681 3f610546 3f000000 -> c02dcfc8 3fabac9b 3ef7a840 3d98d223 bfa0e9c0 be35a764 bf35cc8c 3d489da5",
+        "42199716 c1f5d9f0 c1d0e49e 402b9848 bfd62764 c0238681 3f610546 3f000000 -> c02dcfc8 3fabac9b 3ef7a840 3d98d223 bfa0e9c0 be35a763 bf35cc8c 3d489da4",
         "c1e18843 c1ea1d4a c1f0de9a 40100934 c09a15bb bfa9b9b0 3ea9a9fc 3f000000 -> bfedbc48 4041fa37 3fa3c95f bf2ce41f bfd9b49b 4031a25a 3f95fcaf 3f3ccc46",
         "c1e75efe c247ca30 41917d6c c05f78a5 400ae5d8 bfbb4348 3ee9250f 3f000000 -> 3fbbc938 bf63c8c9 3f5c342f bf6d0d7f 406647ec c00baa52 40070473 3ec14ee3",
         "41ca9c70 c236c993 c1d61825 3f91ebd8 c0156ed7 3d4f0700 3ea50dcd 3f000000 -> be2ded4d 3f293293 be97a457 bedbf082 bda57901 3ea0f91e be104557 3f672d3b",
-        "3f0bac40 c2235044 c12fbf78 bf5d7ee8 bdb4d580 bed6e9f0 3ecc771d 3f000000 -> bcc0b1e6 3b6388d0 3e1d37ca bf60c54b bd30bceb 3bd0b142 3e9032e0 3ef5107f",
-        "c18c5f22 40d0e9c0 c208d1fb c0414db8 bef23af0 be853f10 3f423e80 3f000000 -> 3f9f5cd2 bf89a54c 3fb99ee5 3de3410e 3e101ef2 bcacae1d bf22ac7c beed1c82",
+        "3f0bac40 c2235044 c12fbf78 bf5d7ee8 bdb4d580 bed6e9f0 3ecc771d 3f000000 -> bcc0b1ef 3b6388a9 3e1d37ca bf60c54b bd30bcf4 3bd0b11f 3e9032e0 3ef5107f",
+        "c18c5f22 40d0e9c0 c208d1fb c0414db8 bef23af0 be853f10 3f423e80 3f000000 -> 3f9f5cd2 bf89a54c 3fb99ee5 3de3410e 3e101ef2 bcacae0e bf22ac7d beed1c82",
         "421c97d2 c242f60f 4237a34a c07cedd0 3fa927c0 40be66f4 3e202557 3f000000 -> bf7861a7 3e63b5ad 3fc16f81 3f7971d1 c0868b6f 3f76b1b3 40d19003 be663f9c",
         "41e28214 c1dff8a2 c16675e8 bed18b00 409e6748 3f4e5c30 3e05d941 3f000000 -> bf52ff06 40809974 3f97be2e bebe104e 3ea8b4bd bfcda5f1 bef2a865 bf6db52c",
         "c20c2366 c245663c c214a0c5 c0aad26e 40593d60 3f2dec80 3f366ed6 3f000000 -> c0a9bbed 4081e8c9 3f70011d bd97cbb8 3fa470e3 bf618115 be2e2972 bf7e74d7",
@@ -7300,7 +7300,7 @@
         "420edbd2 4213f8a4 c22eb859 bec6dc50 3ec73660 407b6750 3f6d2051 3f000000 -> 3e9509a0 3f0e98a2 c0241151 3f36d780 be9815b3 bf1182fe 40276c11 3f332da9",
         "c223667d c225ff34 415ea3d4 bf1e8c60 bfaa4c04 3dd5aa80 3e92ff72 3f000000 -> 3f1d6979 bee9bdd3 beff057f be95961a 3e4059d5 be0ecfab be1bd013 3f74d49c",
         "413520a0 420b64b4 41921efc c05b5dc1 4029a30c 401678e8 3de04541 3f000000 -> 3e519ec4 bee0a927 be91cfb8 3f7e59b3 bfe5b178 40762c98 401fc637 3de81f56",
-        "41380bc4 c1c94463 414649dc 40ba1f70 bfcf8424 c0299fe2 3f390b6d 3f000000 -> 3fb61a66 c027a579 c02e92f1 3d09ecb9 40109a20 3f875e20 bc81bf1a be8cb958",
+        "41380bc4 c1c94463 414649dc 40ba1f70 bfcf8424 c0299fe2 3f390b6d 3f000000 -> 3fb61a66 c027a579 c02e92f1 3d09ecb9 40109a20 3f875e20 bc81bf2b be8cb958",
         "c22b966d 4246261a c217aae1 bf82a248 3f91128c c05d921e 3ebb7c1a 3f000000 -> bffbe4d3 403cca92 c0712475 3ef2cfa3 bf87afe1 3fcb6439 c001e544 bf616197",
         "3ee01000 42130f8e c1428140 40bf1842 bfed2720 40828c1e 3e151a3c 3f000000 -> c000583a 3f59d55a bfed76d7 bf6cca17 c09c2c92 40048896 c0907a2e 3ec2983d",
         "c145f42c c0bb08e8 415a04c4 3ecd5a00 3f852b68 3fe922e8 3f51d5d1 3f000000 -> bed83b5f bd89baca 3f6bba4c 3e9cbc6e be0b107a bcb127b4 3e979a44 bf73b5b3",
@@ -7315,7 +7315,7 @@
         "423b1544 4190a20c 40d19768 3dcc3800 3e1ba600 c0beb4e7 3f508cbf 3f000000 -> bfc9acf4 3fdd15a5 be9e6d06 3f11bc01 3fb9246c 3f8f3841 c06379c9 3d2e42ec",
         "c09ae0b8 c23b5550 c13113fc 40a19c44 c0196226 3fd81300 3ebb7d00 3f000000 -> 3f49278a bada5100 bfca8df6 be8e0490 c00bdedd bfb048b4 be6778bd 3e8e0a9c",
         "c1a3ff64 40bda240 40ce6920 3f3f48f0 4063fd30 c052759e 3f0d6d4e 3f000000 -> 3fae6fa2 403c9b58 3dc42885 3f31d2b1 3c8aeb7f 3f7dcaa7 bfe535aa be1c1843",
-        "c1120be8 c1356da0 40f93db8 c05778e2 40821568 40ad9be4 3f6235ac 3f000000 -> 4048150c c001d8cb c0a22786 3ee7fc7e bfcaf663 3e8548d7 4031cd72 3f259945",
+        "c1120be8 c1356da0 40f93db8 c05778e2 40821568 40ad9be4 3f6235ac 3f000000 -> 4048150c c001d8cb c0a22786 3ee7fc7e bfcaf663 3e8548d7 4031cd73 3f259945",
         "c1383fb8 41aa0624 bf90aa00 4098411c c06c4c15 40021778 3f41782c 3f000000 -> c0acf6e7 406374a9 bfdcf47c bd15df43 bea0354c bbffb3e8 bea19208 3f58dcb2",
         "40881408 422378c8 41b17ea8 c0554d28 c091a72f c0a5ce0a 3f7a0e60 3f000000 -> c0101919 bf9ae321 c03ce2bd 3e380a5c bf844d98 bf53e851 bf477512 bf1b3db8",
         "42118818 c0bd7838 42169c9e bffb8898 be3ee040 40a1746c 3f20d3ae 3f000000 -> 3f2bc9d9 bf70eead c034deee 3c6efce6 3efc10da 3f136b94 3f1ef384 3e963716",
@@ -7327,11 +7327,11 @@
         "407510d0 41d12bd8 4238ffde 401f5168 3e0c8260 c068e4c0 3e7e4cff 3f000000 -> 3fd784a2 bfd9df18 bfe8fe65 3ece32b4 3f159759 bfe183d1 bfbcece7 bf435b24",
         "42286d90 c0d669b0 409abdb8 c0a55665 c08b50a6 409d7328 3f0b70f0 3f000000 -> 409f4eb2 3fd59c64 c0a1cfd2 3ebdbccc bf6a8504 c0345791 3fb43350 3f67637d",
         "40808538 420cdda6 c1d96028 3e21ff00 c011ea23 409049de 3ec93506 3f000000 -> bea31741 bf95c98c 3fb2f070 3f5fbbe7 3f7413b0 bf87054b 408474c4 bda142aa",
-        "c186b798 c1346e60 c1c1bc24 c004c3f0 3f7cca10 c0ba966c 3eb25d32 3f000000 -> bf5ea3d5 bf17a594 bf07cc8c bf175dba 3f97106b bce87502 40284694 be111a89",
+        "c186b798 c1346e60 c1c1bc24 c004c3f0 3f7cca10 c0ba966c 3eb25d32 3f000000 -> bf5ea3d1 bf17a595 bf07cc86 bf175dba 3f97106c bce874fc 40284694 be111a86",
         "c1aaffc6 c116eaf8 c1904f01 c0b87841 4006df40 402d2a4c 3f47e57d 3f000000 -> 3fe2a698 bf7fd8cc bf80fca3 bf1c08c1 4085b579 c004ce71 c032ce1f 3f213d89",
         "c210559c c22f40e9 c11f2ce0 bef6b0e0 bf849088 3d4b6300 3f3ac13d 3f000000 -> beaf70e5 bf105e10 be064829 bda9fd9a 3ce9cd31 3d40642e 3c32f36a bf7f1ddb",
         "c11093ec 41e95144 412ac560 c0b81c1f 3ffe6cf8 c0bfec5a 3ecfb1e0 3f000000 -> 3fd42658 bf560945 40677723 be22be66 3f1f2328 3f0f1db6 401a756e 3ee47007",
-        "420bad72 4177dd68 420871a2 402a3910 bfb8db88 40ac257e 3e53a602 3f000000 -> 3da61c89 3f646b2a 403a8407 bd32a950 3e4a2167 bec97eba bf606b11 bf3749a3",
+        "420bad72 4177dd68 420871a2 402a3910 bfb8db88 40ac257e 3e53a602 3f000000 -> 3da61c89 3f646b2a 403a8407 bd32a950 3e4a2167 bec97eba bf606b13 bf3749a3",
         "c14939ec 41a3bbe0 c13f7e3c 40a4cad0 c073b7e8 409996fa 3f22837d 3f000000 -> 406fb95c c04ba0bd 40908492 bf0ed481 c0212a5a 4008e5eb c0425142 bf54738a",
         "c23d1277 c1d90192 c2341210 beec0460 c07243fe 404aa258 3ecd4fb2 3f000000 -> 3ee93428 407a3e36 c04b7377 3e609676 bdd1b1b5 bf61040b 3f36f0e4 3f79c456",
         "41e83d20 42031b24 c232aa82 40982f10 bfc5339c 3ffb17a4 3f6c05e1 3f000000 -> 40812bdf bfe484b2 3fac3cf5 bd1971e8 bf9264b0 beba5e27 bffaa777 bf3604c8",
@@ -9347,7 +9347,7 @@
         "40bcad6c 40779eb8 3af16c3c c174e6b6 3fc0b988 3c801dd6 -> 41a99eb6 401741f4 3c8f63c5",
         "c104d6fa 3f0d0a50 39d9aac2 3fb2d710 bf93689c 3c5a491e -> c11b31dc 3fd9edc4 3c61441e",
         "4197454e 4064df94 3a88e443 c190c1df 3fa35008 39774681 -> 42140396 40133790 3aacb6d6",
-        "c02dbe68 c020dfed 3a6798aa 40824ff8 c04490dc 3bb42404 -> c0d92f2c 3f0ec3bc 3bd151e8",
+        "c02dbe68 c020dfed 3a6798aa 40824ff8 c04490dc 3bb42405 -> c0d92f2c 3f0ec3bc 3bd151e9",
         "c18fdeae 4035f4dc 3d227f08 41778c28 bf9d4c60 399f196b -> c205d261 40824d86 3d23e2cc",
         "4135d448 404c0c34 3c3b1530 410f6126 40668b90 40bb1176 -> 4019cc88 bed3fae0 40bb6f12",
         "c1284539 408de740 38f47fd4 c18045f5 3c53fe00 3a1507ea -> 40b08d62 408d7d41 3a361404",
@@ -12591,7 +12591,7 @@
     {
       "glsl": "float cultmath_cycles_power(float, float)",
       "tolerance": "ulp-bounded, platform pow",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "bfb8bc1c 00000000 -> 3f800000",
         "3f7fc090 3fa15ed0 -> 3f7fb009",
@@ -12854,7 +12854,7 @@
     {
       "glsl": "float cultmath_cycles_logarithm(float, float)",
       "tolerance": "ulp-bounded, platform log",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "416175a4 418f2e6d -> 3f6ac789",
         "40d2d3ad 416ecd13 -> 3f328da7",
@@ -13015,7 +13015,7 @@
         "40f1bf09 4176dd9e -> 3f3d3089",
         "41250305 3f8051c0 -> 446a1e9f",
         "41558518 417a2177 -> 3f7143c9",
-        "404b60bc 4196dad1 -> 3ec99021",
+        "404b60bc 4196dad1 -> 3ec99020",
         "4120edef 4159270a -> 3f629694",
         "4160d238 3ff7d002 -> 408001d4",
         "41870981 4137656a -> 3f944fe0",
@@ -24907,7 +24907,7 @@
     {
       "glsl": "float cultmath_cycles_arcsine(float)",
       "tolerance": "ulp-bounded, platform asin",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "3f74439c -> 3fa22776",
         "beaa06dc -> bead5166",
@@ -24932,14 +24932,14 @@
         "3eae8380 -> 3eb2152a",
         "bf3ff8fb -> bf590ffc",
         "3f7bb06c -> 3fb189e5",
-        "3dee93e0 -> 3def1edd",
+        "3dee93e0 -> 3def1ede",
         "bfb0b96e -> bfc90fdb",
         "bf454824 -> bf613cb1",
         "3f23fb40 -> 3f31f9c7",
         "be9b0000 -> be9d788d",
         "3fb7c110 -> 3fc90fdb",
         "bf0c30e4 -> bf145b51",
-        "3e855c0c -> 3e86ea5d",
+        "3e855c0c -> 3e86ea5c",
         "bf0e2123 -> bf16ae2c",
         "3f72c708 -> 3f9fbe32",
         "3f98afd8 -> 3fc90fdb",
@@ -24970,7 +24970,7 @@
         "3f81d10a -> 3fc90fdb",
         "bf033714 -> bf09c506",
         "3fa3a04a -> 3fc90fdb",
-        "3f1281b8 -> 3f1bfaf3",
+        "3f1281b8 -> 3f1bfaf2",
         "bf34447a -> bf480038",
         "bf9eb144 -> bfc90fdb",
         "3f38d780 -> 3f4e86c5",
@@ -25014,7 +25014,7 @@
         "3f039538 -> 3f0a32b8",
         "3f4cd500 -> 3f6d70e3",
         "3ee655e4 -> 3eeee961",
-        "3ef23d20 -> 3efc5473",
+        "3ef23d20 -> 3efc5474",
         "3e0c9370 -> 3e0d0572",
         "3f9f079c -> 3fc90fdb",
         "3e4b1770 -> 3e4c7278",
@@ -25038,7 +25038,7 @@
         "3f982f94 -> 3fc90fdb",
         "3ef183b4 -> 3efb8213",
         "bed4d500 -> bedb7e63",
-        "bf49041d -> bf672e45",
+        "bf49041d -> bf672e44",
         "bf986f2a -> bfc90fdb",
         "3eeeeb04 -> 3ef89167",
         "bf05421c -> bf0c27dd",
@@ -25087,12 +25087,12 @@
         "bf2114d2 -> bf2e38cf",
         "bf89904b -> bfc90fdb",
         "bf278f84 -> bf36ac3c",
-        "bf7f527b -> bfbfbed2",
+        "bf7f527b -> bfbfbed1",
         "3f8de8c6 -> 3fc90fdb",
         "bfa9dbe0 -> bfc90fdb",
         "bf8e558e -> bfc90fdb",
         "beee0a24 -> bef79347",
-        "bf7c5d15 -> bfb3763a",
+        "bf7c5d15 -> bfb37639",
         "3e2dc4f0 -> 3e2e9d42",
         "3e8c65a4 -> 3e8e3807",
         "3f3be8c0 -> 3f530045",
@@ -25108,7 +25108,7 @@
         "3e8fe798 -> 3e91deba",
         "bf9af793 -> bfc90fdb",
         "3f96f5d6 -> 3fc90fdb",
-        "bf241cb4 -> bf32255a",
+        "bf241cb4 -> bf32255b",
         "bfbff533 -> bfc90fdb",
         "bf02913a -> bf09040a",
         "3f1ad780 -> 3f264ac6",
@@ -25133,7 +25133,7 @@
         "3f700570 -> 3f9b993a",
         "3f68eb8c -> 3f924ad2",
         "bf5ec490 -> bf871d4a",
-        "3f44b0ec -> 3f604fec",
+        "3f44b0ec -> 3f604feb",
         "3e5adaa0 -> 3e5c8e2c",
         "bfb0d056 -> bfc90fdb",
         "3f814c00 -> 3fc90fdb",
@@ -25170,7 +25170,7 @@
     {
       "glsl": "float cultmath_cycles_arccosine(float)",
       "tolerance": "ulp-bounded, platform acos",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "3da419e0 -> 3fbecb6b",
         "bccc7dc0 -> 3fcc41e7",
@@ -25185,7 +25185,7 @@
         "3f99f728 -> 00000000",
         "3efe6a30 -> 3f867f99",
         "bf8e3141 -> 40490fdb",
-        "be1ccb60 -> 3fdcbd17",
+        "be1ccb60 -> 3fdcbd18",
         "bf6312e3 -> 402a57f6",
         "beca9b18 -> 3ffd2360",
         "bfa261f2 -> 40490fdb",
@@ -25221,12 +25221,12 @@
         "3e8561b8 -> 3fa753cc",
         "bf888ac6 -> 40490fdb",
         "3fbb7d54 -> 00000000",
-        "3ec05018 -> 3f97c657",
+        "3ec05018 -> 3f97c656",
         "bf8c0f8c -> 40490fdb",
         "bf72b2f0 -> 40345736",
         "3f244db8 -> 3f5fba77",
         "3f8a5ea0 -> 00000000",
-        "3f792f18 -> 3e6cd374",
+        "3f792f18 -> 3e6cd375",
         "3e8b1738 -> 3fa5d8c1",
         "be22d5b8 -> 3fdd80c8",
         "3f434100 -> 3f340ba0",
@@ -25250,7 +25250,7 @@
         "3f8f186c -> 00000000",
         "3f30b1e8 -> 3f4f1b53",
         "3d953310 -> 3fbfba8c",
-        "bde0dee0 -> 3fd7250d",
+        "bde0dee0 -> 3fd7250e",
         "3f7b8300 -> 3e4007f6",
         "3f35601c -> 3f488ecf",
         "bf9a050a -> 40490fdb",
@@ -25272,7 +25272,7 @@
         "bfb4c70e -> 40490fdb",
         "3e93057c -> 3fa3c820",
         "3f2b8624 -> 3f56293a",
-        "bf51e010 -> 40220aaf",
+        "bf51e010 -> 40220aae",
         "bf8aa06c -> 40490fdb",
         "3f9839c8 -> 00000000",
         "3f28eed8 -> 3f59a156",
@@ -25297,16 +25297,16 @@
         "3e8aea00 -> 3fa5e480",
         "3ed35888 -> 3f9298c3",
         "3f567510 -> 3f13e3ce",
-        "3e9761c8 -> 3fa2a463",
+        "3e9761c8 -> 3fa2a464",
         "3fbc3ca0 -> 00000000",
         "bf5814bd -> 4024d6ee",
         "3f807f68 -> 00000000",
         "3f9dceea -> 00000000",
         "3da55340 -> 3fbeb7c5",
-        "3f1a4008 -> 3f6c92ee",
+        "3f1a4008 -> 3f6c92ef",
         "3fa491d4 -> 00000000",
         "3f385e00 -> 3f44484f",
-        "3e9ac620 -> 3fa1c0e5",
+        "3e9ac620 -> 3fa1c0e6",
         "3e9541ec -> 3fa3329f",
         "bf647da0 -> 402b1eac",
         "3dc1c080 -> 3fbcef2e",
@@ -25351,7 +25351,7 @@
         "beab7798 -> 3ff4c5fc",
         "3f0df694 -> 3f7ba4b1",
         "3f94dda6 -> 00000000",
-        "bf5c7d84 -> 4026f34d",
+        "bf5c7d84 -> 4026f34c",
         "3f9296ba -> 00000000",
         "bfbada1e -> 40490fdb",
         "3f8cf40a -> 00000000",
@@ -25364,11 +25364,11 @@
         "bf6b7605 -> 402f4022",
         "bfad549a -> 40490fdb",
         "3faa5d8c -> 00000000",
-        "3e8b7c88 -> 3fa5be6f",
+        "3e8b7c88 -> 3fa5be6e",
         "3f3fa580 -> 3f398dc6",
         "bf61690a -> 4029746e",
         "bf73a264 -> 403516b7",
-        "bebc692c -> 3ff94c5b",
+        "bebc692c -> 3ff94c5a",
         "bf28f55c -> 4012a9b0",
         "bd6d56c0 -> 3fd07ba1",
         "3e8aae98 -> 3fa5f3ee",
@@ -25427,13 +25427,13 @@
         "3f930316 -> 00000000",
         "bf6bfdd5 -> 402f9730",
         "3fa53312 -> 00000000",
-        "bf1a0e9a -> 400ddba5"
+        "bf1a0e9a -> 400ddba4"
       ]
     },
     {
       "glsl": "float cultmath_cycles_arctan2(float, float)",
       "tolerance": "ulp-bounded, platform atan",
-      "platform": "Microsoft Windows 10.0.26200; .NET 10.0.12",
+      "platform": "Ubuntu 24.04.5 LTS; .NET 10.0.12",
       "cases": [
         "c08cbc16 c1549681 -> c0349aac",
         "418c8108 41948858 -> 3f41f3ee",
@@ -25442,7 +25442,7 @@
         "c1853a3e 4183660c -> bf4ad4c8",
         "40cc3750 c18864ad -> 4032239a",
         "c1841fce 414eb7b4 -> bf682df1",
-        "3f7f11c0 41915dcc -> 3d605f58",
+        "3f7f11c0 41915dcc -> 3d605f59",
         "c1190690 40822148 -> bf959a14",
         "41235546 414a8e7c -> 3f2db91b",
         "c173027e 4157ae48 -> bf584be7",
@@ -25451,12 +25451,12 @@
         "41504298 c1432d3c -> 4014b8bf",
         "41976732 4165afb0 -> 3f6bff17",
         "c12faa83 c19c5692 -> c0284d67",
-        "c0aa038c c0cb2194 -> c01c7633",
+        "c0aa038c c0cb2194 -> c01c7634",
         "c0df2a78 c0a67120 -> c00d8b25",
         "4144767c c11a39a5 -> 400f2006",
         "c00c8aa0 4194be56 -> bdf0c4af",
         "3f876310 c1937378 -> 404564aa",
-        "41636814 c1172a84 -> 400a13e1",
+        "41636814 c1172a84 -> 400a13e2",
         "3f81e2e0 bd4f6800 -> 3fcf71a7",
         "41309010 c08f8f1c -> 3ffa7c90",
         "40982a9c 3f904760 -> 3fab4541",
@@ -25467,23 +25467,23 @@
         "4192314a 4086f2c0 -> 3fac080a",
         "411b37ca c171da02 -> 40248b70",
         "c1664f18 c130242c -> c00e512f",
-        "40eced38 40bd9198 -> 3f655f43",
-        "4104386c 411d5130 -> 3f32ed71",
+        "40eced38 40bd9198 -> 3f655f42",
+        "4104386c 411d5130 -> 3f32ed70",
         "bdd98800 c15cd654 -> c04891c6",
         "c161bae2 c19f6675 -> c021a16c",
         "c15bccb4 4139d89a -> bf5e709e",
         "c1065de6 c1860dc7 -> c02b5428",
         "419a2318 416c82f8 -> 3f6a973f",
-        "bf911740 3eafb040 -> bfa36fa5",
+        "bf911740 3eafb040 -> bfa36fa4",
         "41961b7c c01fd768 -> 3fd9fffb",
         "4042f5d8 c00cea20 -> 400c95f1",
-        "c12f053d 418e307c -> bf0d3c4b",
+        "c12f053d 418e307c -> bf0d3c4a",
         "403d4400 c11dc866 -> 40366a62",
         "c15831c7 412e7716 -> bf644dcc",
         "c0d29330 41698de0 -> bed8d810",
         "c0fd3872 415963f8 -> bf0702af",
         "c131bb1f c074e670 -> bff386a5",
-        "417f6828 40a71880 -> 3fa09869",
+        "417f6828 40a71880 -> 3fa09868",
         "40497b80 41717390 -> 3e529a28",
         "413af82e c196608f -> 40257713",
         "4179eb80 bfb8a2f0 -> 3fd4d959",
@@ -25492,8 +25492,8 @@
         "414f2488 c180a1ba -> 401dad4f",
         "4036b5f0 c15671f1 -> 403ba162",
         "bf97a3d0 c0046bb8 -> c027c818",
-        "40ae84d8 c0f9a4b6 -> 402203eb",
-        "3feb4440 40f9d6e0 -> 3e6cc1c6",
+        "40ae84d8 c0f9a4b6 -> 402203ec",
+        "3feb4440 40f9d6e0 -> 3e6cc1c5",
         "419f7088 411a15a2 -> 3f8f723b",
         "c188441a bfeff970 -> bfd71812",
         "40560bd0 410fd5de -> 3eb65b86",
@@ -25508,10 +25508,10 @@
         "414c9fc4 418893dc -> 3f249745",
         "c033b3b8 c18b7729 -> c03ed777",
         "c13f3667 c152d7a7 -> c019eb30",
-        "c086fb50 41627eb4 -> be9446b9",
+        "c086fb50 41627eb4 -> be9446ba",
         "c13dde75 41858b9e -> bf1e348f",
         "41655ddc c13d8347 -> 4010b9bb",
-        "40a95660 41584940 -> 3ebf0aa3",
+        "40a95660 41584940 -> 3ebf0aa4",
         "4141fbc4 c0ce1146 -> 4003c77a",
         "c0091050 c155ea5c -> c03ee580",
         "40b8f0c0 c18079b9 -> 4032f416",
@@ -25524,17 +25524,17 @@
         "40a7d388 c07a5f68 -> 400d8c45",
         "4186baee c161afee -> 4011273b",
         "c1988920 3f471480 -> bfc3d822",
-        "3f70c440 40be95d8 -> 3e2060d0",
+        "3f70c440 40be95d8 -> 3e2060cf",
         "417834e8 415d5098 -> 3f57b555",
         "c1775234 40c0f8f8 -> bf99734e",
         "c1974114 4198ffc8 -> bf479800",
         "410c0ec4 bff12930 -> 3fe432a6",
         "413a6dc4 c09ce414 -> 3ffc0b0b",
         "be987ac0 c097edfc -> c0450d7e",
-        "bfa53460 4194fa8e -> bd8db6e1",
+        "bfa53460 4194fa8e -> bd8db6e0",
         "40d38cc8 c19c290d -> 403429aa",
         "415e9230 bea6b840 -> 3fcc0ec1",
-        "c1612e94 4199eb08 -> bf21ad99",
+        "c1612e94 4199eb08 -> bf21ad98",
         "c102419c 3f3e0580 -> bfbd6c6a",
         "c171e10c 3e75cd00 -> bfc70799",
         "c159f7c3 c040e368 -> bfe4ee5c",
@@ -25543,18 +25543,18 @@
         "c0ebecc4 4188a552 -> bed0a0ee",
         "40b612c0 419e96ba -> 3e8f1b96",
         "c1392859 c184cf09 -> c02219d5",
-        "40f88828 c0379bc8 -> 3ff65a7c",
+        "40f88828 c0379bc8 -> 3ff65a7b",
         "4183657e 418c205a -> 3f40d57c",
         "3d64c400 c049c398 -> 4047eda0",
-        "c184e5e2 c0ba5c6c -> bff438b3",
-        "c13cf1d2 c09df406 -> bffbbd40",
+        "c184e5e2 c0ba5c6c -> bff438b2",
+        "c13cf1d2 c09df406 -> bffbbd3f",
         "41951ea0 40d3e958 -> 3f9d5e14",
         "4117a1c4 4182e3fa -> 3f0666f9",
         "c100421b 3fa11c00 -> bfb52067",
         "c0a4c048 3fd9b1a0 -> bfa0392a",
         "c0bce6f0 c0a756e0 -> c012ed67",
-        "410f31a8 4089ad2c -> 3f8fb3f9",
-        "beb17800 40836d64 -> bdac6ea4",
+        "410f31a8 4089ad2c -> 3f8fb3fa",
+        "beb17800 40836d64 -> bdac6ea3",
         "c0724d88 bee688c0 -> bfd836b1",
         "3fb83bc0 c1693dec -> 4042c367",
         "c18c3dd4 4027c610 -> bfb60fc6",
@@ -25562,7 +25562,7 @@
         "41231d74 404d91d0 -> 3fa1fe4e",
         "c0e92c5a c04e1b80 -> bffe543d",
         "404ffd08 c1396f46 -> 403790b4",
-        "bf50eb60 41702f48 -> bd5e7501",
+        "bf50eb60 41702f48 -> bd5e7502",
         "c0294f90 412b4d2a -> be780e6d",
         "c0fe6df0 41350240 -> bf1cd3f4",
         "bfd3b0d0 41824f24 -> bdcf3ab0",
@@ -25571,15 +25571,15 @@
         "400eab20 c180166a -> 4040354a",
         "40b741d8 415a8318 -> 3ecb4b31",
         "c0b19f72 c1844941 -> c03455ba",
-        "418bd268 c0f5d76c -> 3ffe1263",
+        "418bd268 c0f5d76c -> 3ffe1262",
         "3fa6a0a0 c19bf37a -> 4044cb60",
         "417687a4 418fb914 -> 3f357bee",
-        "c104b28d 40b23950 -> bf7abba9",
+        "c104b28d 40b23950 -> bf7abbaa",
         "40b00cb0 be7bb000 -> 3fcec6d5",
         "41836b9a c15bc2b2 -> 40111937",
         "40697890 417344c4 -> 3e7121a8",
         "4190121e c158f0df -> 400dd562",
-        "c18bdd8b bf6a2c00 -> bfcfc0be",
+        "c18bdd8b bf6a2c00 -> bfcfc0bd",
         "418b5438 4191f240 -> 3f431ff0",
         "c0f7e4e4 410571fe -> bf3f9e8f",
         "c163d334 bd98d600 -> bfc9bb97",
@@ -25590,27 +25590,27 @@
         "c133cbd1 c12c03ab -> c015618c",
         "bf32bb00 c1111506 -> c04424d8",
         "40e3794c bfa93e10 -> 3fe099e8",
-        "419cd3d2 bf1c60c0 -> 3fcd0c97",
+        "419cd3d2 bf1c60c0 -> 3fcd0c96",
         "bf800240 40cf58c0 -> be1ccef2",
         "c1630418 4194bc52 -> bf26e0ae",
-        "419ee38a c0d13810 -> 3ff1c4a9",
+        "419ee38a c0d13810 -> 3ff1c4a8",
         "c0554ad8 bf756f80 -> bfecea8c",
         "4155c1e0 c086c8b0 -> 3ff02782",
         "c19438df c155bc54 -> c00c82ae",
         "4181ed52 c072d0e0 -> 3fe66fdc",
         "41335fee c12dcd2f -> 4015c95e",
         "c1571882 c194fd20 -> c0210be4",
-        "c19a88b4 c0b6e8d0 -> bfede310",
-        "c153621e c19b2864 -> c022ca68",
-        "40a5abdc 419f6cf2 -> 3e822342",
+        "c19a88b4 c0b6e8d0 -> bfede30f",
+        "c153621e c19b2864 -> c022ca69",
+        "40a5abdc 419f6cf2 -> 3e822341",
         "40d30c58 419f1e6c -> 3ea3ee9c",
         "418c0490 c0b33c62 -> 3ff0b4e5",
-        "c0831f14 40e27288 -> bf065d69",
-        "bf2ad860 4075b2b0 -> be303f56",
+        "c0831f14 40e27288 -> bf065d6a",
+        "bf2ad860 4075b2b0 -> be303f57",
         "bf04a640 bffc8c00 -> c038a00e",
         "bf41b3a0 40b8c260 -> be056f50",
         "4021d860 c14d4bd9 -> 403c9ba3",
-        "3d83a000 40cb8cf8 -> 3c258914",
+        "3d83a000 40cb8cf8 -> 3c258915",
         "c178b13e c0fba980 -> c0028267",
         "c0108e98 40935624 -> bee9826e",
         "40833c68 40d08ed0 -> 3f0fc87b",
@@ -25623,13 +25623,13 @@
         "c1000d87 419fc51c -> bec32579",
         "c0814a50 c18dda43 -> c03ab943",
         "c186e3b7 c15b7765 -> c0103ce8",
-        "4183a496 c01779a8 -> 3fdb58d3",
+        "4183a496 c01779a8 -> 3fdb58d2",
         "40e51c20 bfe49ed0 -> 3fe85ad7",
-        "4187b382 c1690142 -> 4011ef13",
-        "40d37970 419b19ac -> 3ea83332",
+        "4187b382 c1690142 -> 4011ef14",
+        "40d37970 419b19ac -> 3ea83333",
         "3fa7f3f0 c0b5afc8 -> 403a86cd",
         "c122c32b 416a72a0 -> bf1b5a62",
-        "40374b70 c19b6a93 -> 403fb1c3",
+        "40374b70 c19b6a93 -> 403fb1c2",
         "c08588a0 c19f609e -> c03bd8f2",
         "419cbe90 c170df46 -> 400e75e0",
         "4182e2b4 c1643109 -> 40126ac4",
@@ -25642,9 +25642,9 @@
         "c1300d51 c108ac40 -> c00ec793",
         "410261e6 c1588362 -> 40265f3f",
         "419adcac 40054e48 -> 3fbb5784",
-        "41798160 c0ecc4b0 -> 4000e25f",
+        "41798160 c0ecc4b0 -> 4000e25e",
         "40639318 c1702fdd -> 403a2d2c",
-        "c1794797 c1829f3b -> c0184bc9",
+        "c1794797 c1829f3b -> c0184bca",
         "c0904192 c0035a40 -> bfffbf67",
         "41787da0 c19a2a35 -> 401da5e0",
         "4120e654 c1014c4b -> 400fdab9",
@@ -25664,15 +25664,15 @@
         "4112e32a c18e9f42 -> 402aa0a2",
         "bfaa2d50 40ef51f8 -> be3427dc",
         "c16ae95c 406f7cb0 -> bfa91e64",
-        "40d2db80 405037e8 -> 3f8e5b82",
+        "40d2db80 405037e8 -> 3f8e5b81",
         "be920280 419b18c2 -> bc70fbde",
         "41823e9c c10676ec -> 4003074a",
         "40fc01e0 40a9689c -> 3f7a9c4a",
         "416ade10 c15a3b2c -> 40147298",
         "c12b4626 419bd752 -> bf00a1ec",
-        "413a29aa c0cd07be -> 4004beff",
+        "413a29aa c0cd07be -> 4004befe",
         "c199d0c3 c1866487 -> c0127d6a",
-        "419e0288 c1425a56 -> 4007d1b3",
+        "419e0288 c1425a56 -> 4007d1b2",
         "4144a97c 4083fd0c -> 3f9f9ec3",
         "4104e2a2 3f327440 -> 3fbe57fd",
         "c10cd1b9 40378e30 -> bfa0bd4e",
@@ -25685,7 +25685,7 @@
         "3fc08c60 c177750c -> 4042db49",
         "c10a43a9 c0be1246 -> c00b121d",
         "4061f8c0 40e4294c -> 3eeb6b1a",
-        "c0aa3df6 4165c098 -> beb5a9cf",
+        "c0aa3df6 4165c098 -> beb5a9ce",
         "c13c904c c1220f4d -> c011f7c3",
         "4141fe18 c13691ef -> 4014db0f",
         "c043e348 40bf5874 -> bef239e5",
@@ -27502,7 +27502,7 @@
         "41849800 c188d01c 41c72b04 bdd28ae4 beedfee5 bf837164 3f90e18e 3f3f55f0 00000000 3b0d2fc8 4236f87d bf39e059 3f2e8b81 3f74e94f 409bab14 4004ea5c c0dfa028 3f15b8f0 40bd0658 40f00d4c c03d5e5d 3fd6171b 3f14477a 00000008 4023bcd8 beb3a626 -> 3c1191c1 bb1feb74 3c0b933a 3f428fb6 3da36fdc 00000000",
         "422b6520 41258304 c0839c80 bf7be9f9 bf5e6f5d be832d17 3fb0ec81 3db71d93 3f000000 bab888e5 3d2777da bffc2caa 3fcdc7ff bfbf07b1 bfad3168 406be260 c0b132a1 3f177070 3f3a7250 c03e6f00 402b13e6 403e9444 403f1752 00000005 3fc9b537 3e80067b -> ba77e11a 3bb8a89f bae78866 3f9248c4 3e00dfe5 3aeaa69b",
         "41d93ec4 422da77c c2100d66 3f52fd44 3febeba3 3fa7c7f0 401c2757 3fd15b5a 3ca3d70a c08b04fe 3c9ab5f4 3f64b957 3f00166b 3e8499d1 c0318716 c0d2f8c4 c03076c4 40aaf1a8 bee4d250 c01196bc bf93badc bfc7a3c4 401329e9 00000003 4038f474 bf67d4d5 -> c56ce0f4 c5053dc2 c4891c8e 3f0ccf21 4d38aa8b 48af23ac",
-        "c1929f8e 41790590 bd960400 401c4ee9 bef7d899 bf905fa8 40316b2a 3ec68420 3dcccccd 3e2351d4 3d82509f bf11a5ca be6aff5d 3e360e5b 3fb5bef8 406b31b0 bf6c5108 be5bcca0 3f9523a8 be3fd840 bfbe3742 3f6faee8 bf6227f9 00000004 3fd683e2 3f187ba5 -> 40594069 3f65417a bed6c66a 3f9fc888 455dd8dc 43679f26",
+        "c1929f8e 41790590 bd960400 401c4ee9 bef7d899 bf905fa8 40316b2a 3ec68420 3dcccccd 3e2351d4 3d8250a0 bf11a5ca be6aff5d 3e360e5b 3fb5bef8 406b31b0 bf6c5108 be5bcca0 3f9523a8 be3fd840 bfbe3742 3f6faee8 bf6227f9 00000004 3fd683e2 3f187ba5 -> 40594256 3f654700 bed6cbe8 3f9fc85b 455dd8d8 43679f29",
         "40653cc0 41fa519c c2431b4d 3eec3129 3fc4bc98 bf3584e5 3fe13e56 3e87c466 3ca3d70a 4047c965 3d3a6a63 bf948db3 bf1fca65 bf84aa3d 40f42854 c0860ed1 3fb75a08 40ed70ea 40a2e562 3fa437d0 bfe25dd3 c0025cd0 3e6a13b4 00000007 bf12ee58 3f7ada76 -> c363268b c2e25afd c34d34a0 40995dd9 48bcadde 42ffb11b",
         "42060ba2 c2181a78 41e2e484 3f9298b5 bfd5ea1c bf6b356e 4048300d 3fe741dc 3f000000 3b27c028 423a8cc6 bec5937d 3f22c857 3f807614 3fe5bac8 40d1014c 40e06ba6 c034bf4c 40a3aa92 40217fb8 40396fc4 3df08d77 3fb28b80 00000003 40099c68 bf32bfca -> bb131d2c 3b94b2a7 bb43e70f 3f9c4e3e 3b4883f5 3c04918b",
         "41d5de38 c1ada306 42039892 bfdd6bd1 bfaa73dd bee8d71e 403bc376 3fb43217 3f000000 3a946acd 3f963133 be85f94a becba2e1 be643b88 c0aa4450 bfdf4a84 40c9c04e c0131930 bf47dfe0 3f835170 bf538f19 be8d9115 40279934 00000007 3f031cfa be896c82 -> 3a026a39 39981093 ba5dbea0 3e3ebb35 3836a673 00000000",
@@ -30586,7 +30586,7 @@
         "bf217c8d becc21d0 bf378e33 42c53108 bf217c8d becc21d0 bf378e33 42c53108 00000000 3f800000 bf217c8d becc21d0 bf378e33 42c53108 00000003 -> bf217c8d becc21d0 bf378e33 42c53108 bf217c8d becc21d0 bf378e33 42c53108 00000000 3f800000",
         "c167ddc0 c1f40f78 4320be2c 45d2bda6 00000000 00000000 00000000 7149f2ca 00000000 bf800000 42a6931d 407c8e40 42a61cd5 4547a8c8 00000001 -> 42a6931d 407c8e40 42a61cd5 4547a8c8 c167ddc0 c1f40f78 4320be2c 45d2bda6 3f800000 00000000",
         "00000000 00000000 00000000 7149f2ca 00000000 00000000 00000000 7149f2ca bf800000 bf800000 c1e4e8a0 c25b8dec c2ce2346 4556aa42 00000000 -> c1e4e8a0 c25b8dec c2ce2346 4556aa42 00000000 00000000 00000000 7149f2ca 00000000 bf800000",
-        "3fcb389c bfa59b47 bfe3cb28 4386cf30 c1a79864 c2560988 c241c9a4 44ae6380 3f800000 00000000 3fcb389c bfa59b47 bfe3cb28 4386cf30 00000002 -> 3fcb389c bfa59b47 bfe3cb28 4386cf30 3fcb389c bfa59b47 bfe3cb28 4386cf30 3f800000 40000000",
+        "3fcb389b bfa59b45 bfe3cb26 4386cf2f c1a79864 c2560988 c241c9a4 44ae6380 3f800000 00000000 3fcb389b bfa59b45 bfe3cb26 4386cf2f 00000002 -> 3fcb389b bfa59b45 bfe3cb26 4386cf2f 3fcb389b bfa59b45 bfe3cb26 4386cf2f 3f800000 40000000",
         "00000000 00000000 00000000 7149f2ca 00000000 00000000 00000000 7149f2ca bf800000 bf800000 430dced8 c2d3b8a0 41c3f5b8 45f4e96b 00000000 -> 430dced8 c2d3b8a0 41c3f5b8 45f4e96b 00000000 00000000 00000000 7149f2ca 00000000 bf800000",
         "00000000 00000000 00000000 7149f2ca 00000000 00000000 00000000 7149f2ca bf800000 bf800000 c30244bd c314b27a c2241c9c 461f3b8e 00000000 -> c30244bd c314b27a c2241c9c 461f3b8e 00000000 00000000 00000000 7149f2ca 00000000 bf800000",
         "00000000 00000000 00000000 7149f2ca 00000000 00000000 00000000 7149f2ca bf800000 bf800000 3f8ec21f 3f13a3d0 be7dd51e 42b950fc 00000000 -> 3f8ec21f 3f13a3d0 be7dd51e 42b950fc 00000000 00000000 00000000 7149f2ca 00000000 bf800000",
@@ -31739,7 +31739,7 @@
         "c241a5e0 c242c597 42392e04 414ffe88 4023300a bf62a529 3eee0f01 3fe1f6fc -> 43b0ba3f",
         "422ef81c c1df9090 42443a20 412d9f04 403fa01d 3f800000 00000000 3ff5ec9e -> 42f03d17",
         "3f3ba9c0 c2065cd8 411c377c 4130b954 3f880d5a bf4d8570 bf18a234 40000000 -> 429ddaeb",
-        "423f58a4 421bad6e c2017fe6 42049b00 3fe0e102 3f730bed 3ea0cd6c 40000000 -> 438a1045",
+        "423f58a4 421bad6e c2017fe6 42049b00 3fe0e102 3f730bed 3ea0cd6d 40000000 -> 438a1045",
         "421528b0 c12f9154 bff1f060 c19f606d 40394317 3c84c589 bf7ff764 3f9fda01 -> 42eb70b5",
         "c0c9f1d0 c1ff8201 41930284 423d7824 4014f92e 3e2ea92e bf7c3fa3 3fe891f4 -> 43a26e90",
         "c1aff82e 42362f0e c20a0a82 421c50da 409a8f72 bf77edad be7f1b90 3ff535ca -> 42ffe7e4",
@@ -31749,7 +31749,7 @@
         "41c22940 c2226c3b 4240d7d8 c0e640f8 3fee023b 3f309945 bf3955a5 40000000 -> 42a0a558",
         "4101000c c20202a0 c1c65c5f 401ad230 4010b5de 3f800000 00000000 3f82e782 -> 42db292c",
         "4238f014 c1353b20 4230369e 421d4a3a 3fb64c6a bf41167c bf281629 40000000 -> 42d48aed",
-        "40f22198 421a67a6 c0304a50 c09d7d38 3facaeed 3f02ccdc 3f5c0fe2 40000000 -> 42e9280d",
+        "40f22198 421a67a6 c0304a50 c09d7d38 3facaeed 3f02ccdb 3f5c0fe2 40000000 -> 42e9280d",
         "c14c405c 409f0e80 c1bb6a8f 419f6660 4080cd72 bf76da65 3e87a3cd 40000000 -> 42f79358",
         "41b5e980 c1109a54 c212bc33 c15cf3e0 3f5b2c4b 3f800000 00000000 3fc58ca2 -> 429d3f4a",
         "413fda1c bfc75060 421e896e c12ea118 403abfae 3f24b7d1 3f43f825 3fa75c45 -> 42b224aa",
@@ -31814,7 +31814,7 @@
         "c236f7ed 42046a80 c0241130 c22a15e6 3f5bb68e 3e9cddfc bf73b04e 3fec480e -> 4307e250",
         "41d3a9e8 418e3f0c c022fbf0 c190f0fd 408f5ad8 3e866a80 bf77053a 3f800000 -> 434ec062",
         "422626aa 42135cae c0b544d8 4210cafa 406fb8b4 bf651957 3ee4785d 3fe13313 -> 43900f90",
-        "41f77da0 c1d1ad5f c130b9f0 c2201c58 40874837 3dff44da bf7e00ed 3fffa9f1 -> 4344dac5",
+        "41f77da0 c1d1ad5f c130b9f0 c2201c58 40874837 3dff44db bf7e00ed 3fffa9f1 -> 4344dac5",
         "c22f19db c11a44c8 c19df0ae c1a1832e 403f4c53 3f305e7b bf398d98 3fbc5ee3 -> 42dd66af",
         "41866588 42018b8c c2402dd9 42048e9c 407a09d4 3f800000 00000000 40000000 -> 43fd5765",
         "41c625c0 c1df1259 42419630 c18ef0e8 3f46721c 3f800000 00000000 3ff12cdc -> 420d7e7d",
@@ -31850,7 +31850,7 @@
         "c0b637f0 4229f3be c2254d84 41da9a94 40979af7 bf0700b3 bf59825c 3f8bc50f -> 4342e7e3",
         "c092fbd0 c20cdb54 41876478 4107a440 40371a08 3f4fab7b bf15b278 3fe3b6ee -> 430f7138",
         "422f59f0 c1ec1e44 c1d66859 420dc7dc 4045e6b5 3ed67732 bf687578 3f800000 -> 43945fe6",
-        "418b1ca4 c143fb68 41f55428 c1eedf89 40860f17 be4f6c00 bf7ab16c 3fb41876 -> 42dcb882",
+        "418b1ca4 c143fb68 41f55428 c1eedf89 40860f17 be4f6c01 bf7ab16c 3fb41876 -> 42dcb882",
         "c136992c 41993670 421dffe6 c2266742 4027610a 3f800000 00000000 3f800000 -> 434f4d1d",
         "41e27824 c0d40888 416a1630 c00e0860 400a3eb1 bf7ecc92 bdc62375 3f800000 -> 41f8552e",
         "41b2922c c1d473e5 c12ee5a0 c1d2001c 408cd97e 3ef75a98 3f602491 3f9dcc68 -> 431ab6db",
@@ -31883,7 +31883,7 @@
         "c226672c 4228b7d0 c0643e40 c227b7cc 40793355 3ecd0113 bf6a9553 40000000 -> 4433b414",
         "c1329d70 c190dddf 41123968 c11c2b30 405fd881 3f800000 00000000 3fa1b017 -> 42bca94f",
         "c21ec9a9 c22a158f 41a6eb80 420bddfc 3fd25826 3f800000 00000000 3fe74e34 -> 435c5c38",
-        "c17a2b70 c20dcaa8 40b6d428 c1c0f90b 407d478a 3f3473f4 3f35957f 3f800000 -> 42bf48ed",
+        "c17a2b70 c20dcaa8 40b6d428 c1c0f90b 407d478a 3f3473f3 3f35957f 3f800000 -> 42bf48ec",
         "41c11e6c c1c7ab81 c1711f94 c1bc0ffe 3feb2042 3f74bb33 be963c18 3ff3fa68 -> 43060788",
         "c11a57a0 c2126e3a c212c484 422f59ca 4090d354 3e763cf2 3f787d00 40000000 -> 4429ff94",
         "41aa06e0 c2138faa 4097f5e8 c1d48a4f 40604e08 3f54107b 3f0f676a 3fc6eb20 -> 42977bd7",
@@ -31914,7 +31914,7 @@
         "c22b9c5d 41a3b104 c197c2ff c222deb0 40953a5e bebfb5a0 bf6d6087 3ff0acd2 -> 43ea5723",
         "c1c72483 c1fc4b00 41fb8aa8 c1ef21ff 403d3d56 3d3fee95 3f7fb803 3fc4db88 -> 43274db0",
         "c21e7c78 c227bbc8 420cd268 c13f73b0 3fe00e01 3eb286db bf6feef5 3fa3ba41 -> 430d1ed6",
-        "c2328b6b c1c2c75e c202aa31 42091558 404fff58 3f70ecad bead1b02 3ffedec6 -> 43483e38",
+        "c2328b6b c1c2c75e c202aa31 42091558 404fff58 3f70ecad bead1b03 3ffedec6 -> 43483e38",
         "c0936308 c19d7289 c0127d90 419470dc 3fd9448e 3f800000 00000000 3f83c35a -> 42820e6a",
         "c1b74ac9 41f59e70 421fca6e c2228d4f 4075178e 3f7f763d 3d84b8e0 3fe0a51a -> 43f2aec0",
         "c23cb659 4198811c c0ea6d50 c157b264 404a1262 3f0a1893 bf578efe 3fb33134 -> 435df931",
@@ -31967,9 +31967,9 @@
         "c1ba5631 c210962f c207c687 41a40a2c 3f353506 bf2d1e64 bf3c96da 3fda92fe -> 425404e3",
         "4218f4f0 41807434 c21c9271 bf7d8540 407cd98d 3f36af04 3f3356ef 3f800000 -> 439c8676",
         "c219e678 422c9750 c1e0fd63 c2422d52 404fbf8a be6a50ea bf79352f 40000000 -> 440f42c5",
-        "40399060 420c36f0 c2382b58 c017cb90 408781f9 beeb6749 bf635661 3fc570b8 -> 43be5581",
+        "40399060 420c36f0 c2382b58 c017cb90 408781f9 beeb6748 bf635661 3fc570b8 -> 43be5580",
         "c176f0f0 42269078 c12f94a0 41c8e7dc 3f059596 3f7f89e2 bd75ce7c 3fdf3440 -> 411cfbf7",
-        "41df7c04 c2224749 c2394013 41c0602c 407b7334 bef71fd3 3f6034c6 40000000 -> 443896a6",
+        "41df7c04 c2224749 c2394013 41c0602c 407b7334 bef71fd2 3f6034c6 40000000 -> 443896a6",
         "41a042a4 c22f6797 41623c30 c2210ce8 404ad116 bdca8b58 bf7ebeb6 3ff88d32 -> 41d7a18a",
         "3fdc1000 c1b59af3 40bb8a58 40f5cfe0 3f3c7436 be953fc5 3f74e1c9 3f800000 -> 41b494df",
         "c153d970 4239b5bc 422cfd5a c159699c 40956f4b bef64eb5 bf606e45 3f82f38c -> 43c0de04",
@@ -31989,262 +31989,786 @@
       "glsl": "float cultmath_lattice_smooth_step(float, float, float, float)",
       "tolerance": "ulp-bounded",
       "cases": [
-        "40c5238e 40c6bf1a 40c50e44 3bfe6c0c -> 40c5238e",
-        "4098f6f7 40a039ec 4098ecd3 3b2e761f -> 4098f6f7",
+        "4043f529 406662e2 40366a88 3f1ea0cd -> 4044374e",
+        "40c17e48 40cbce9f 40a9d8d7 3f3d2b88 -> 40c17e48",
         "40960ea4 40b20934 40823fc7 3f39909c -> 40960ea4",
-        "410e873c 4122b260 410ae28f 3f538fa2 -> 410e873c",
-        "40e20722 40fe6d61 40e07aa2 3f0d4f03 -> 40e20722",
-        "4076247a 40936e36 4063df84 3e92701b -> 4076247a",
-        "40a5a053 40b7a7b7 40a2a437 3ea81bff -> 40a5a053",
-        "4040ce90 40ad48d9 4038d15a 3f800000 -> 4040ce90",
-        "409e3e4b 409f852c 409de7a2 3ccec516 -> 409e3e4b",
-        "40a8d2b2 40b05c4a 40a44745 3e41504c -> 40a8d2b2",
-        "408125ed 40855604 4059c51f 3f800000 -> 4080e8d9",
-        "407ee87a 40c842b4 4079bb52 3f3e11d2 -> 407ee87a",
-        "4082e243 4095462c 4082ddff 3ac57122 -> 4082e243",
-        "40f0a2a9 4104bf2b 40e91485 3f0b903e -> 40f0a2a9",
-        "40ddd6a1 40e1c265 40db8d84 3ddacb43 -> 40ddd6a1",
-        "410836e5 410b6766 4106d43f 3ddb9ab8 -> 410836e5",
-        "40e5a65c 4104fa0d 40c9b228 3f800000 -> 40e5a65c",
+        "40d3b649 40db5755 40c3319d 3f5e8dc8 -> 40d46116",
+        "40a0626a 40c9f744 408e575d 3f6e7f9d -> 40a0626a",
+        "40d51fd9 40e67c59 40d51011 3bc44d35 -> 40d51fd9",
+        "40484b40 409ae7f5 4035cfea 3f800000 -> 40484b40",
+        "4091ff58 40986ff6 408fe35c 3e08c998 -> 4091ff58",
+        "40f9710c 41015b58 40e2bc55 3f35a5ba -> 40f9710c",
+        "40fb9f31 41185dde 40f0bbbd 3f800000 -> 40fb9f31",
+        "408390bd 40900557 40835df2 3bdb835e -> 408390bd",
+        "402978c9 4087a632 400f4c63 3f800000 -> 402978c9",
+        "40ddd2a2 4100f71c 40da33c5 3eb45994 -> 40ddd2a2",
+        "40acfd8a 40b536fd 40960fa6 3f376f1e -> 40acfd8a",
+        "40dfd6ee 40db6410 40d5f0d9 3ebbf29f -> 40db6c62",
+        "401af9df 40290f96 3ffd20ba 3f4f34f1 -> 401c0985",
         "40bf567d 40bfca3f 40bf45af 3c14e242 -> 40bf567d",
-        "40576b3c 4070005f 40546e0e 3dbfca5c -> 40576b3c",
-        "4096a166 40a5e84d 4089f2cd 3edfabfe -> 4096a166",
-        "41179132 411da29f 41178a11 3b1e1254 -> 41179132",
-        "410a4648 41291892 4107fda6 3f800000 -> 410a4648",
-        "41181a6f 4128cb90 4116e90a 3f0f142f -> 41181a6f",
-        "408c1a50 409cd275 40873dec 3eabab63 -> 408c1a50",
-        "40842cf0 409fa919 4061eb5b 3f3acdae -> 40842cf0",
+        "407458de 408d0c54 40546e0e 3f800000 -> 4076e7f4",
+        "3fcc6f8f 3ff8fa8d 3fc3aa24 3edfa15d -> 3fcd0b32",
+        "40f16811 40ff96c8 40e6ecd0 3ec54fbd -> 40f16811",
+        "40c0ebc0 40e7ca4d 40c07989 3e1aefe4 -> 40c0ebc0",
+        "4083d12f 40929512 40524a2d 3f5560c6 -> 4083d12f",
+        "410bbdcb 41165b91 410b87c2 3eeac2c9 -> 410bbdcb",
         "411180c5 411c37d2 410b2e95 3f1a7f90 -> 411180c5",
-        "3f777fe5 3ff01510 3f777994 3b99168e -> 3f777fe5",
-        "40ce05a8 40f6089e 40b6089e 3f800000 -> 40ce05a8",
-        "409aa29d 40b7ec53 409a901a 3c08c454 -> 409aa29d",
-        "3f83a956 3f844795 3f8351b1 3b75e444 -> 3f83a956",
+        "40c10875 40c13c00 40c06f40 3dd87aea -> 40c07ce0",
+        "40ff572f 4118e754 40efe260 3f800000 -> 40ff572f",
+        "4069f1e2 40859e42 4069cb5c 3e8e550f -> 4069f1e2",
         "403699c9 40374cee 4036494c 3c01d11b -> 403699c9",
-        "409eaa19 409eaa3a 409e69b0 3c14e758 -> 409e980b",
-        "40492428 40b0a7c4 4028e1a2 3f7288e8 -> 40492428",
-        "402b6c29 4050d12a 401d3f70 3ea13623 -> 402b6c29",
-        "410f0927 4129c7ff 410b32ca 3f6955d7 -> 410f0927",
-        "4109e1f8 410b34e5 4109cb04 3bc7215f -> 4109e1f8",
-        "40813b37 40aea868 4073f91b 3f50508c -> 40813b37",
-        "41018662 411f20c4 40fe0df2 3f800000 -> 41018662",
-        "407ced65 4097b3d0 406b0862 3f04b9f3 -> 407ced65",
-        "411095a8 41095702 4106ac7b 3f43df9c -> 4109c3a9",
+        "403569f4 4061ee1e 402047de 3f0005e2 -> 403569f4",
+        "411f4e0c 412baec3 411f46b6 3bbe9b13 -> 411f4e0c",
+        "40bc26f9 40d1c4e5 409e36c0 3f6f81cb -> 40bc26f9",
+        "402de374 404f03d1 4020d431 3f5f0cdd -> 402ff4b1",
+        "411ce7e2 412ab20a 4116ae3f 3ef55f4f -> 411ce7e2",
+        "40326bc6 4032f6bb 4032104d 3be66dd1 -> 40326bc6",
+        "40ad037d 40bb2ef6 40ab9080 3e287e94 -> 40ad037d",
+        "40f5c2f9 411e4e9f 40f41529 3f4bf498 -> 40f5c2f9",
         "3f7dba59 3f9cfe0f 3f7db21a 3bfdf6d3 -> 3f7dba59",
-        "3fef1587 3ff20833 3fee7a04 3c638ba1 -> 3fef1587",
-        "3fd8d28f 3ff2d660 3fc1124e 3e446547 -> 3fd8d28f",
-        "406f1eb2 40aa27ee 406016b8 3f341820 -> 406f1eb2",
-        "411ea8bc 412e3d8d 411e10af 3f0ec6d2 -> 411ea8bc",
-        "3efa9e03 3ef809b0 3ef69e40 3ddf51c5 -> 3eeec589",
-        "405331ac 4095876d 404001b1 3f134f1b -> 405331ac",
-        "40b88a82 40e8037a 40a9ed62 3f785861 -> 40b88a82",
+        "400d1bb7 40773d02 3fee7a04 3f800000 -> 400d1bb7",
+        "401e7444 40612778 3fc1124e 3f800000 -> 401e7444",
+        "411b2e53 41201f88 4116f8b5 3eb69929 -> 411b35a0",
+        "3f099ecd 3f87f065 3e7e1d75 3ed0596c -> 3f099ecd",
+        "40c81663 40cd243e 40b75118 3f062a5b -> 40c81663",
+        "40cf4050 40db015a 40b6c38f 3f43e604 -> 40cf4050",
+        "40abc5c5 40cbbe2d 40a8e16b 3f069aef -> 40abc5c5",
         "40df659f 410d2ffd 40da5ffa 3f800000 -> 40df659f",
-        "3fe1e762 402c702e 3fde1255 3d5ce99c -> 3fe1e762",
-        "408f3a98 409f869b 4087fcc0 3ebc4ed9 -> 408f3a98",
-        "40a1bdb3 40b30b16 40980702 3f70206f -> 40a2efa2",
-        "3fbad23e 3f7de5f4 3f4ac582 3f800000 -> 3f84cc3f",
-        "41108627 4123237f 4104a90a 3f6c7044 -> 41108627",
-        "4110be86 4121cdde 410f68f9 3dbbbea0 -> 4110be86",
-        "410c7c67 410e6988 410bf2a7 3d8557d7 -> 410c7c67",
-        "40109f5b 407906fa 40063ad6 3f800000 -> 40109f5b",
-        "40a11b4b 40dbd4e5 409e4eba 3f182fcb -> 40a11b4b",
-        "3f8715aa 400c4b6c 3f7a4d27 3f1b7044 -> 3f8715aa",
-        "4051bdeb 4076de26 40206ef5 3f800000 -> 405459fe",
-        "4082ecba 40a1e94d 405b2d2c 3f4c3189 -> 4082ecba",
+        "40129023 408aa761 3fde1255 3f800000 -> 40129023",
+        "401c736e 40505622 401c2955 3b9e180a -> 401c736e",
+        "4050a38c 407597f9 404f1d6d 3e99ea31 -> 4050a38c",
+        "40f01eed 411716ed 40d596b8 3f800000 -> 40f01eed",
+        "40cc2500 40e89186 40b50fae 3f4e0761 -> 40cc2500",
+        "411f4b0e 412faff7 41128cf4 3f691816 -> 411f4b0e",
+        "40abff2a 40e54906 40a54906 3f800000 -> 40abff2a",
+        "40e7c32b 40f9944b 40e4578a 3e2edc17 -> 40e7c32b",
+        "411315a8 411654f5 4111a383 3f800000 -> 41134f96",
+        "404347a2 4060453a 40206ef5 3f0b62b3 -> 404347a2",
+        "4108266f 411298e4 40fe9676 3f1e02ab -> 4108266f",
         "40c1da6c 40db2367 40b2ed1a 3f800000 -> 40c26444",
-        "40cd6b22 410328a6 40b40fab 3f800000 -> 40cd6b22",
+        "41131a8f 411d4802 41069a2b 3f480644 -> 41131a8f",
         "3f9417a3 3fb99c91 3f93ea2d 3c00839c -> 3f9417a3",
-        "412adb42 413bb935 411dc576 3f6f9df5 -> 412adb42",
-        "41235978 4142bf25 411aacb0 3f4a4d48 -> 41235978",
-        "4088d3b8 4094a2a2 408486f5 3f018267 -> 40891c9d",
-        "411bdda5 412560de 4115b0d0 3f112774 -> 411bdda5",
-        "40253e07 402a94df 40242a9f 3d4d47f8 -> 40253e07",
-        "40fda622 410aab4b 40f6baf3 3efd9db5 -> 40fda622",
-        "40a11065 40c35e11 40824618 3f800000 -> 40a11065",
-        "410d46b7 41154a8e 410d3b0b 3c021362 -> 410d46b7",
-        "4093278d 40a29431 408da924 3eb1a41b -> 4093278d",
-        "4062dd79 40620147 4062cf6e 3b5c8b16 -> 40620147",
-        "3f99abc6 402051ee 3f3f721e 3f800000 -> 3f99abc6",
-        "3fff7784 3ffff4c3 3fff6456 3b106ce3 -> 3fff7784",
-        "407cbd85 40a1ef63 4043dec6 3f800000 -> 407cbd85",
-        "408b8875 40abf777 4062a606 3f6a91d0 -> 408b8875",
-        "40a7a2e0 40ae53b4 40a1fb11 3e458a28 -> 40a7a2e0",
-        "40c8b2e8 40dbab83 40c7b76b 3dadb5d8 -> 40c8b2e8",
-        "3f1a287b 3f5197a2 3eb9120e 3f800000 -> 3f1ea619",
-        "40ceb97d 40de7055 40c749ae 3eb3fa29 -> 40ceb97d",
-        "40b058bb 40af4879 40b054af 3b711460 -> 40af4879",
-        "404e6c36 405a905d 404e631d 3a8facc5 -> 404e6c36",
-        "40c6b957 40deb2b4 40c4b56a 3da243cd -> 40c6b957",
-        "3fb12c88 4005dfa7 3fb10ed1 3bd502f0 -> 3fb12c88",
-        "40a13122 40c68291 4088503f 3f800000 -> 40a13122",
+        "3ff7149e 4065a576 3f939788 3f7c7845 -> 3ff7149e",
+        "40e86afb 41055a1a 40db8d2d 3f7889b9 -> 40e86afb",
+        "410c76c8 411b7e10 410c6bff 3b5e32ce -> 410c76c8",
+        "3f3223d0 40081e7f 3ecf79e6 3f5dd3ed -> 3f3223d0",
+        "40ca97a8 40f917d4 40c7ead6 3f45f86a -> 40ca97a8",
+        "411a0cdd 411a354e 4119f37f 3c039dd2 -> 411a0cdd",
+        "4073f036 4088ad25 4065bec8 3f003e7d -> 4074056b",
+        "40a6c0b5 40de57d4 409e57d4 3f800000 -> 40a6c0b5",
+        "402420de 40412d25 40230003 3e71690f -> 402420de",
+        "401c6ff1 40513c26 4016961a 3eea9831 -> 401c6ff1",
+        "3fa37526 3fcaa15a 3f24eb97 3f21feb4 -> 3fa37526",
+        "40b92451 40d2cdf7 409aeca1 3f71bd7e -> 40b92451",
+        "41171d7a 4117e26c 410f0420 3f800000 -> 41167a2e",
+        "410ddd1e 41132859 40fd11ae 3f754473 -> 410ddd1e",
+        "4068e296 40963d06 4067a419 3f09abe5 -> 4068e296",
+        "4041ea2c 405c4a7c 401a0ea3 3f800000 -> 4044c5a8",
+        "40496c66 4089836c 403db027 3f2a1dce -> 40496c66",
+        "403046f1 403b6648 400bfa5f 3f113248 -> 403046f1",
+        "40a5f81f 40a532fa 40a21350 3e4ab2ae -> 40a48daf",
+        "4089ae55 40842af4 40715f54 3f4c03bf -> 40845b14",
+        "3f6e3e16 40137a80 3e90c51f 3f800000 -> 3f6e3e16",
         "4107707f 411ee37a 41076623 3f3beab8 -> 4107707f",
-        "40ddd6b2 40f5510a 40d7517d 3e5dadec -> 40ddd6b2",
-        "4028308a 408392ab 4006cdac 3f7c21f6 -> 4028308a",
-        "40c85dba 40dcff0e 40c851e9 3ae460ee -> 40c85dba",
-        "40a7e690 40bc31e8 40a74bf3 3d3bd8ac -> 40a7e690",
-        "3fcf27c2 3fecbd19 3fce7182 3bf259dd -> 3fcf27c2",
-        "40678676 40ae2955 405be7c6 3f800000 -> 40678676",
-        "3f309621 3f7b276e 3f1bcddf 3e3eb31e -> 3f309621",
-        "4091ddd2 409200e3 4091d9db 3b1c1fe8 -> 4091ddd2",
-        "41103c76 411246e2 410e7df6 3df23ae8 -> 41103c76",
-        "4117c4e8 412dc177 4110d054 3f67891a -> 4117c4e8",
-        "4027929c 40299219 40273fa2 3bd4c5c1 -> 4027929c",
-        "409943ed 40c36078 4092c287 3f4105bb -> 409943ed",
+        "40ccf5d2 40eb69bc 40ccde63 3be73492 -> 40ccf5d2",
+        "4115ce83 411aeace 4115cccc 3ba671b5 -> 4115ce83",
+        "4109e0f8 4105cb03 41047684 3f25bf7c -> 41061634",
+        "402dc0dd 40317167 401e80d7 3ed5b92d -> 402c60f3",
+        "40298954 4045e9f8 3fe2f1cb 3f6041b9 -> 40298954",
+        "40825601 408e1c2e 4081f767 3e424c78 -> 40825601",
+        "4031a5d2 4043aab6 4003b2cc 3f37cc19 -> 4031a5d2",
+        "409fa325 409fbcdb 409f8e81 3b39696d -> 409fa325",
+        "4123a056 41309260 411440cf 3f75f876 -> 4123a056",
+        "402581fd 403646e7 40255fbc 3bae8400 -> 402581fd",
+        "41002bb5 4112577d 40f07b99 3f561263 -> 41002bb5",
         "40345ff2 40755452 400cb504 3f66e41c -> 40345ff2",
-        "407f0c4c 40ab67fa 406c4c64 3f550720 -> 407f0c4c",
-        "40c07dab 40c11918 40c069e8 3bfdabbf -> 40c07dab",
-        "408d09ff 409e50a4 408c533c 3e8feb3e -> 408d09ff",
-        "411b0b06 411adb69 4112ab64 3f4c3df7 -> 411a0210",
-        "411f8fff 412967c1 411f8baa 3b97586a -> 411f8fff",
-        "410060ef 4100a426 410052fe 3c225042 -> 410060ef",
+        "40017ba3 401e9df4 3fdef61f 3ec044b2 -> 40017ba3",
+        "40479514 40592621 40476a65 3bc2a938 -> 40479514",
+        "411c5754 41230df4 4113b4c8 3f0a28be -> 411c5754",
+        "40d8753b 40de9afb 40d1e934 3e5219a5 -> 40d876d4",
+        "406577f7 4096b3ac 4061c64d 3e726141 -> 406577f7",
         "407315fa 4073a652 40730fa2 3b96afdf -> 407315fa",
-        "40cdef82 40ce0e00 40cdec0d 3ac19e8e -> 40cdef82",
-        "3e255061 3fa5c88c 3cafac30 3f2309db -> 3e255061",
-        "40970a93 40de3aac 4087b45a 3f7a5d4d -> 40970a93",
-        "411d94d1 41299c53 411abe05 3eede4e5 -> 411d94d1",
-        "40215404 40635a10 401f0d84 3f065d0b -> 40215404",
-        "3ee2c640 3fbdff1b 3ec5ff4c 3d893467 -> 3ee2c640",
-        "3ea4e56c 3f260b3c 3e7df6ec 3f5d7253 -> 3eb590b4",
-        "411ee2f2 412518e7 411ae243 3ebd9a75 -> 411ee2f2",
-        "40902ea4 40b8ae3f 4071e347 3f800000 -> 40902ea4",
-        "3fee6290 407bcb04 3fb8b068 3f6bdd78 -> 3fee6290",
-        "3fbcea8c 403bfb7f 3f6fedfd 3f800000 -> 3fbcea8c",
-        "41172715 4117351c 411721c3 3b1acb1e -> 41172715",
-        "410f5ae0 41204b33 410ddb59 3e16f558 -> 410f5ae0",
-        "3dd3f73c 3f473510 3d4c244b 3ec280ac -> 3dd3f73c",
-        "402e3b9b 40769446 402c45ef 3f13c66a -> 402e3b9b",
-        "40eff1e8 4106fc11 40efd4b3 3bb0b6a6 -> 40eff1e8",
-        "41024e8d 4112550e 40f3940f 3f66ffb0 -> 41024e8d",
-        "405a4ec7 405c6e7f 405a3d74 3a9ebc02 -> 405a4ec7",
-        "40bc7211 40d22c76 40ac732e 3f16e51e -> 40bc7211",
-        "3f840e9f 3f9dbc78 3f70eb5b 3e177614 -> 3f840e9f",
-        "40124351 3ffdf13a 3fd938e8 3f759bc4 -> 400115b4",
-        "411098d9 41276038 410db3a1 3f4d64b5 -> 411098d9",
-        "411266b5 413337ee 410bd60e 3f7d1a62 -> 411266b5",
-        "4103e3ac 410cba86 41000a49 3ecb03d6 -> 4103e3ac",
-        "41200baf 4123de4a 411ff45b 3c11cbd8 -> 41200baf",
-        "4106099a 4106417c 410606d6 3bea9729 -> 4106099a",
-        "41198930 411a8fcc 411987b5 3b4f59d4 -> 41198930",
-        "40e22b67 41006093 40d2e604 3f376c86 -> 40e22b67",
+        "40d70fc5 4106fc68 40cdec0d 3f800000 -> 40d70fc5",
+        "3fc656eb 3fc86462 3fc549e4 3c469f88 -> 3fc656eb",
+        "4117f737 412bfb15 41125b11 3f4374ce -> 4117f737",
+        "4082286d 40ac217e 4074691a 3f800000 -> 4082286d",
+        "409a4b62 409f2189 409a32f8 3d9dd22e -> 409a4b62",
+        "40c2fc75 40ae1e63 40abfda8 3f572f53 -> 40ae96e8",
+        "4122a133 412721b6 4119f1e1 3f0af51c -> 4122a133",
+        "40d867a1 40d96528 40d82c8e 3c9c4d0c -> 40d867a1",
+        "40c55842 40bb8854 40b02f1a 3f3a9b74 -> 40bc573f",
+        "3f8114c8 3f99cfc9 3f6fedfd 3e076329 -> 3f8114c8",
+        "411fedb6 413721c3 411721c3 3f800000 -> 411fedb6",
+        "411804f5 413892b6 410ddb59 3f800000 -> 411804f5",
+        "4102198b 410130e7 4102175b 3a88f388 -> 410130e7",
+        "40bb3f1b 40bb7a2b 40bb3360 3b8d957e -> 40bb3f1b",
+        "4120fcee 4126675a 4115158c 3f534e76 -> 41217e78",
+        "40bd346c 40e01580 40bcca7d 3f0d2c0b -> 40bd346c",
+        "411406cd 412aea05 410bb12e 3f7772a9 -> 411406cd",
+        "40cc960a 40d7ed98 40af0476 3f6c8c9e -> 40cc960a",
+        "4077cca9 408b8547 4048ff78 3f3b34c4 -> 4077cca9",
+        "40ff6416 4103a530 40fbe5e5 3e3647b2 -> 40ff6416",
+        "40204245 40760226 4004802c 3f6303f5 -> 40204245",
+        "41092ed9 411dbea9 410445b4 3f494001 -> 41092ed9",
+        "40e22431 41020cd2 40c22685 3f800000 -> 40e22431",
+        "4001b675 4037f65f 4001a078 3bdd8727 -> 4001b675",
+        "40431ecc 40673ca3 4019e107 3f24f714 -> 40431ecc",
+        "408398fa 409d90f1 4083479c 3dfc5115 -> 408398fa",
         "40b01c8b 40b03a21 40b01b90 3af48a62 -> 40b01c8b",
-        "40a9ed91 40cc814f 409df955 3f3a1fe8 -> 40a9ed91",
-        "40c53a89 40f00d4b 40b42081 3f6a35f8 -> 40c53a89",
-        "40bf67fc 40bfec0a 40bf4a12 3c21f7f7 -> 40bf67fc",
-        "4098b804 40bb2855 407cace7 3f800000 -> 4098b804",
-        "40a349ac 40a1bcce 409b8cf2 3f1db8b1 -> 40a0b707",
-        "40c45572 4107ea0f 40c3c9be 3f3b95fb -> 40c45572",
-        "411e22fa 4127f1ba 41199be3 3ef9986c -> 411e22fa",
-        "407e3175 40944129 407dddcf 3eaa920f -> 407e3175",
-        "40e9bf5c 40eb6ef0 40e86cb8 3d408dee -> 40e9bf5c",
-        "40e0777d 40f33ba0 40e0714f 3b4e5bf8 -> 40e0777d",
-        "3d9cda7e 3da352d2 3d9b189d 3b03a351 -> 3d9cda7e",
-        "40986c28 40bd705e 407845de 3f800000 -> 40986c28",
-        "40865f3b 409a69cb 40839f86 3eb65229 -> 40865f3b",
-        "41150524 413ec39c 41101b23 3f800000 -> 41150524",
-        "40c347e1 40f38b0a 40bf01c8 3ebdcbb9 -> 40c347e1",
+        "3f96acfc 3febc639 3f38a720 3eff59ca -> 3f96acfc",
+        "40bb14e2 40bd4576 40baed48 3c048022 -> 40bb14e2",
+        "3f7480d4 3fa94dc0 3e8a72ed 3f2f475d -> 3f7480d4",
+        "40a9bf78 40b91793 408fd5be 3f537f93 -> 40aa45b0",
+        "40bea191 40cf12ee 40a85a18 3f323bcb -> 40bea191",
+        "3f9445fb 3fd292ea 3e6e51ff 3f76d36e -> 3f9933f7",
+        "40c672c7 40d91721 40b9c149 3f800000 -> 40c7bf34",
+        "40b9e8a1 40bf258b 40a9a9dc 3f01f62a -> 40b9e8a1",
+        "4117ea58 412bca7d 410cb17a 3f800000 -> 4117ea58",
+        "402d6551 404cecef 402d46a3 3e7d3262 -> 402d6551",
+        "401993d4 4031e894 3fd7d085 3f36ae44 -> 401993d4",
+        "40c9c7db 40feb443 40c682a6 3f6295da -> 40c9c7db",
+        "41184f17 411ec718 41101b23 3f033f3a -> 41184f17",
+        "40697819 40937941 40692d30 3b9eea23 -> 40697819",
         "408ab4cd 408a4a11 408aae79 3bdf81de -> 408a4a11",
-        "4008291c 402bb48a 400767b7 3eaf9900 -> 4008291c",
-        "40bfe0fe 40e90c93 40b2ebf4 3f800000 -> 40bfe0fe",
-        "4120b5a8 4120b262 4111939b 3f800000 -> 411fb404",
-        "405d4e9d 4097f74e 40586103 3e8ea463 -> 405d4e9d",
-        "40a92fde 40deecec 40a4db0b 3f684785 -> 40a92fde",
-        "410ae763 411929da 4105fd4c 3f800000 -> 410afdec",
+        "4107af4c 4106819d 4107ad79 3b3e534b -> 4106819d",
+        "40921d62 40a5ef95 4081925f 3f1174d7 -> 40921d62",
+        "40cc7663 40cc2357 40cc3143 3c1bd992 -> 40cc2357",
+        "41110b70 4111dd8b 4111065d 3c081b1a -> 41110b70",
+        "410548f6 410d37cb 40ed2bca 3f6b310a -> 410548f6",
         "4118fac5 4121f599 4111930e 3f03145b -> 4118fac5",
-        "410aa44b 41114d12 410a996c 3bebf1f7 -> 410aa44b",
-        "409ccb96 40d2647e 4094f69a 3f75b791 -> 409ccb96",
-        "40808027 40bb507c 4076a0f9 3f800000 -> 40808027",
-        "40541b7c 40a4d380 4049a700 3f800000 -> 40541b7c",
-        "4056b98e 407ee610 4054ffce 3e9fcd58 -> 4056b98e",
-        "3fde3570 40037b02 3fd2642a 3e524765 -> 3fde3570",
-        "4025d50e 407d77f0 40199b3b 3f47b96b -> 4025d50e",
-        "402d9bf7 404f693a 4010a932 3ef44a1f -> 402d9bf7",
-        "3daa222a 3da4e03c 3d66b508 3d72590c -> 3d8db733",
-        "4039e35d 404c9bdf 402e2eba 3e7ae59a -> 4039e35d",
-        "3f7361f2 3fe9e334 3f1ab6c6 3f1a4d4d -> 3f7361f2",
-        "40e38d76 40e08c31 40dfdaf2 3e37ebb5 -> 40e08512",
+        "40eb839a 41052d36 40d3878b 3f5e19ef -> 40eb839a",
+        "402490c9 402a4f32 402331da 3d63ab06 -> 402490c9",
+        "3f6e524a 3f9b8850 3eb3273d 3f14beab -> 3f6e524a",
+        "40ba6ceb 40c36af1 40a7cfcc 3f14e8f7 -> 40ba6ceb",
+        "3f5d868b 3f8848d7 3f5d25f3 3c12eaff -> 3f5d868b",
+        "40981314 40a9dbce 4080e18c 3f398c3c -> 40981314",
+        "403e0c6f 4053b382 401cb508 3f055d9b -> 403e0c6f",
+        "41113e48 41208c51 41113d3a 3baa143a -> 41113e48",
+        "3f94e77d 3fda27b9 3e5d6945 3f7274a8 -> 3f94e77d",
+        "406ad14e 406c4bf6 406ab230 3b621008 -> 406ad14e",
+        "409775e4 40b881e0 40815770 3f800000 -> 409775e4",
+        "41177681 411babf4 4109ddd5 3f598ac7 -> 41177681",
         "4078e4d0 409e6630 405bccf2 3f4ea5ff -> 4078e4d0",
-        "4100cabe 411b4c46 40f61f38 3f800000 -> 4100cabe",
+        "405c34a6 4080625d 402397ed 3f6272e3 -> 405c34a6",
         "411e957d 411eae61 411e919c 3b662a72 -> 411e957d",
-        "4106080b 4121c862 41041899 3f6d7e46 -> 4106080b",
-        "40e25175 410d68fa 40dc9dd5 3f800000 -> 40e25175",
-        "40f9971e 41051543 40f7cd70 3f27a5e7 -> 40f9e2fe",
-        "406eda17 40b2edbe 4067e62a 3f800000 -> 406eda17",
-        "40ed4507 41069b5d 40e2e293 3f293ec5 -> 40ed4507",
-        "41004bda 41044e70 40f8bb63 3e7e17c3 -> 41004bda",
-        "40eed6a2 40e437f2 40e213f6 3edad1bc -> 40e462da",
-        "3fab77e2 4010ad98 3f944892 3ee6f818 -> 3fab77e2",
-        "40968bbe 40bde4cc 408c0d1a 3f800000 -> 40968bbe",
+        "3f5ad660 401ef168 3f542bf0 3f53ccd9 -> 3f5ad660",
+        "3ff727a2 400b1a54 3fe41108 3e45328a -> 3ff727a2",
+        "3eacf8eb 3eae4c26 3eacc6ca 3ae7b616 -> 3eacf8eb",
+        "40f1f5c5 410467a3 40d2760b 3f7bfdd2 -> 40f1f5c5",
+        "41220917 412bbcf4 411bde13 3efdee18 -> 41220917",
+        "40c3002f 40d49b42 40a32958 3f7eb6b5 -> 40c3002f",
+        "41155ef3 411d1122 41154943 3d3b34d4 -> 41155ef3",
+        "3f6f42af 3fc6d18a 3f3918e7 3ed0a4ca -> 3f6f42af",
         "4112b13a 412058be 4112af16 3b54a3b2 -> 4112b13a",
-        "3fa85e3b 4008f47c 3f953a7c 3e8d9dba -> 3fa85e3b",
-        "4085a885 408fc316 40824848 3e57ace0 -> 4085a885",
-        "40801e9c 40b0e42e 4061c85c 3f800000 -> 40801e9c",
-        "3f8dc4df 407afed6 3f80e79a 3f800000 -> 3f8dc4df",
-        "4024182a 405a313a 4023f2a5 3b93933a -> 4024182a",
-        "411f26fe 41227daf 411ad3bf 3f26560c -> 411f5ac5",
-        "4008d0a1 40610320 40069f5a 3e89388b -> 4008d0a1",
-        "408a4a2b 408fb056 40803075 3f67e9d0 -> 408a716e",
-        "40cf9907 40e26a58 40cd6d9a 3e9b3b96 -> 40cf9907",
-        "3fd02008 403ab220 3f2c62fa 3f800000 -> 3fd02008",
-        "3e7fd5e2 4009aa32 3e06550c 3f800000 -> 3e7fd5e2",
-        "4016cf9c 4054ecdf 401662b0 3da076fe -> 4016cf9c",
-        "4104b578 4105a129 41032201 3dcf5b20 -> 4104b02a",
-        "40e22d83 40e7f8bd 40dff8b7 3d9b8c73 -> 40e22d83",
-        "40c77201 40dc5812 40ae0871 3f800000 -> 40c886a4",
+        "4100dba7 4109850c 4100d5a6 3b064cec -> 4100dba7",
+        "3f9e06bd 3fd41bb9 3f07f090 3f341cea -> 3f9e06bd",
+        "3f79c586 3faf9476 3e993ae9 3f2d2812 -> 3f79c586",
+        "4110b725 41187d87 4107e8e6 3f0ce3f6 -> 4110b725",
+        "408fe86d 4098ae0c 407925ba 3f1aac82 -> 408fe86d",
+        "411fcdcc 413ad91e 411b77b4 3f036e85 -> 411fcdcc",
+        "40ea5350 40f4aa4e 40d3ab35 3f3540dc -> 40ea5350",
+        "411f24a6 4123ac62 41131ded 3f406b94 -> 411f24a6",
+        "40e3c40a 40f94109 40df3b89 3ed02bfd -> 40e3c40a",
+        "409c98e5 40a3d169 409c90a3 3bde172f -> 409c98e5",
+        "41047c0e 410fa820 40ef54f7 3f4d1928 -> 41047c0e",
+        "40a9c4e5 40b8050a 40998f29 3f01addd -> 40a9c4e5",
+        "3fbcc938 3fe910f4 3f30bf9e 3f48d2d2 -> 3fbcc938",
+        "409c145c 409fa156 40999d3f 3dc082ee -> 409c145c",
+        "4126dc2c 411edbef 411ba956 3f800000 -> 411f94ed",
+        "3f284bf6 3fc48821 3f272a10 3c163c9f -> 3f284bf6",
         "3fc3a086 4041bff0 3fb46e95 3ec552da -> 3fc3a086",
-        "40b56669 40db5cc7 409cda49 3f800000 -> 40b56669",
+        "40a48468 40adff09 408cacb1 3f3ebdb7 -> 40a48468",
         "40941a12 40944e36 40940a31 3b828bbb -> 40941a12",
-        "40d96af3 40dca1e8 40d64ca1 3f0de64b -> 40d90c4e",
-        "40b990d7 40eb6d94 40ab6d94 3f800000 -> 40b990d7",
-        "4084faef 408b493a 4084a9e7 3dea1f25 -> 4084faef",
-        "40a01ddd 40a8c9f1 40a004b8 3bb18cda -> 40a01ddd",
-        "409ee6c1 40d996f1 409a6111 3f380b79 -> 409ee6c1",
-        "3f32cf18 3f9823e8 3ef698b4 3ebfd5d5 -> 3f32cf18",
-        "4103169d 41132ba5 41020912 3ea5aa88 -> 4103169d",
-        "403f9833 40ac1ddf 4031eb58 3f800000 -> 403f9833",
-        "40ed33d4 40f5342c 40ed3342 3aa09a76 -> 40ed33d4",
-        "410323f1 411967ee 40ffee30 3f4b86b3 -> 410323f1",
-        "409abf42 40bb9b92 407e1b68 3f743d82 -> 409abf42",
-        "40903aa4 40b30cf8 407bee26 3f2ecec9 -> 40903aa4",
-        "4041022c 40948799 402f3c46 3f6fa058 -> 4041022c",
+        "410e9c05 41224081 410cb762 3f2c48fb -> 410e9c05",
+        "3f9fba1e 3fd7443b 3ef5c403 3f44923b -> 3f9fba1e",
+        "40876ebb 40c3b051 4084a9e7 3f800000 -> 40876ebb",
+        "40ede6c1 4100f278 40e13a68 3f014b6b -> 40ede6c1",
+        "4109bf65 4117d3fd 4101a4d3 3f317951 -> 4109bf65",
+        "411f7cd8 4134207d 4113d7fe 3f800000 -> 411f7cd8",
+        "40d126e5 41055374 40d00f28 3f6a5f01 -> 40d126e5",
+        "4031e8bd 4075720f 4008c090 3f5e1835 -> 4031e8bd",
+        "411b79c9 41284e41 411b7874 3ac5e3f0 -> 411b79c9",
+        "4126b37c 412e4dbb 41189370 3f6200b8 -> 4126b37c",
+        "4100f60f 41073bb7 4100d1cf 3c1623ec -> 4100f60f",
+        "411f08e7 412b79e3 4115a9c1 3f325960 -> 411f08e7",
         "40e36775 4108282b 40e04d04 3f7e42c5 -> 40e36775",
-        "40da4d33 40de4872 40da1c20 3da06d24 -> 40da4d33",
-        "40d30664 4100a38a 40c163e3 3f800000 -> 40d30664",
+        "40dc8e97 410c8616 40da1c20 3f800000 -> 40dc8e97",
+        "408ded4c 409cfdea 406883ce 3f4d5b28 -> 408ded4c",
         "402d8fcf 402eca7b 401dc025 3f05bea5 -> 402ae57c",
-        "40ad193a 40d73997 40973997 3f800000 -> 40ad193a",
-        "3f961d97 4059d26d 3ef3e87d 3f800000 -> 3f961d97",
+        "404dc3f2 406f3a7f 401ea496 3f3c7d70 -> 404dc3f2",
+        "40ca3a85 40d911f5 40b97765 3f061903 -> 40ca3a85",
         "40a5ebcd 40dececb 409ececb 3f800000 -> 40a5ebcd",
-        "4098703f 40c7ae24 40906167 3f5967f5 -> 4098703f",
-        "406b7e37 406d8cbb 406b77ff 3b80543b -> 406b7e37",
-        "407e7348 408a3637 4075f4e7 3e64af3d -> 407e7348",
+        "4046351b 4063ed1a 403f9ddf 3ee9d194 -> 4046351b",
+        "410595d8 4105adf6 41058e62 3b7c9c0c -> 410595d8",
+        "409ad8fd 40acb0b8 4084b2de 3f3130fb -> 409ad8fd",
         "40aae3c5 40c42753 40a67bc9 3f0a7cf7 -> 40aae3c5",
-        "3eea003c 3f968d96 3e5afbc2 3ef65c3b -> 3eea003c",
-        "40e745f7 4102e522 40cb226e 3f7231fa -> 40e745f7",
-        "40239ed6 404afa8a 400ba868 3ed3e49f -> 40239ed6",
-        "41097d41 4122e0fa 4102e0fa 3f800000 -> 41097d41",
-        "410b9a8c 411c2b4a 4105253a 3f383084 -> 410b9a8c",
-        "3ec8ff98 3feb1004 3ebfac5a 3f0a936d -> 3ec8ff98",
-        "410e0dd1 4113887c 410da648 3e519a9f -> 410e0dd1",
-        "40860b7d 40a73fa6 406dd92e 3f414c3c -> 40860b7d",
-        "40d9f8e2 40da2128 40d9e699 3b6a3ce8 -> 40d9f8e2",
-        "411df44d 4124a137 4112cd3f 3f800000 -> 411eac03",
-        "410483d9 4107785e 41046402 3c0c733e -> 410483d9",
-        "408d9062 40c98c40 4082d51f 3f4391eb -> 408d9062",
-        "400c768c 402dbfa3 4007374b 3e9db076 -> 400c768c",
-        "3f7a49a6 3f816408 3f276aa8 3eac7ec6 -> 3f736b12",
-        "40a4ac2a 40ac0363 40a49658 3bc1d4a6 -> 40a4ac2a",
-        "411c3e95 4139d619 411a7211 3f800000 -> 411c3e95",
-        "40a1169f 40a12cd7 40a113ec 3ac755f7 -> 40a1169f",
-        "41283320 413de8de 411a0bbc 3f7dba50 -> 41283320",
-        "40fea4ef 41004967 40fe8d5b 3b90d158 -> 40fea4ef",
-        "40cb8868 40e0446d 40ca1fc9 3d501162 -> 40cb8868",
-        "407b8d7d 407c2ae1 407b22e4 3bde6c26 -> 407b8d7d",
-        "3fee6667 3fcec518 3f8ab6c9 3f68e9a8 -> 3fd1b9fa",
-        "3fe6da2a 401104c1 3fe6c775 3bfb901f -> 3fe6da2a",
-        "400b331d 40531cdf 4005e9f5 3f1d52c9 -> 400b331d",
-        "40cba5de 40fd0dd6 40c2f4fa 3f703ed8 -> 40cba5de",
-        "40eb341a 4107ddd2 40e8ae20 3f1c3610 -> 40eb341a",
-        "409e3afc 40cdbbab 409aec1d 3f537be6 -> 409e3afc",
-        "4110c7f0 411e1fa7 4104f60f 3f494cc0 -> 4110c7f0",
-        "3fc9df1a 403ea8d6 3f7deac5 3f800000 -> 3fc9df1a"
+        "3f8658b4 3fd63ee2 3f8292ec 3cff5ad9 -> 3f8658b4",
+        "41153c59 411d3178 4114b6a2 3e19319f -> 41153c59",
+        "3fee6a52 3ff671d6 3fbe8550 3f67d949 -> 3fea4ced",
+        "40199dc5 40875ebd 3ff9f3c4 3f55765b -> 40199dc5",
+        "40fa333e 410130c9 40e0a64b 3f4c6796 -> 40fa333e",
+        "410fa018 412cde5a 410da648 3f800000 -> 410fa018",
+        "4006dfab 402535d4 3fffe954 3ec17ef3 -> 4006dfab",
+        "40e52c68 4103e814 40c7d028 3f800000 -> 40e52c68",
+        "4039ea32 406f49ba 40398fb8 3bee54ff -> 4039ea32",
+        "41265aef 4131e6c4 411719f0 3f740fea -> 41265aef",
+        "409264b9 40a6f898 408c7988 3f601d51 -> 409307d2",
+        "40fa1320 40f80836 40f9fd53 3b5e8bdc -> 40f80836",
+        "409a9dd1 40ae4f24 40767c58 3f7afd27 -> 409a9dd1",
+        "40976d3b 409f4698 40901ab3 3e72be4b -> 40976d3b",
+        "406371bc 4063a312 40636125 3b03d9b3 -> 406371bc",
+        "41159d5e 411e52af 410be175 3f1bbe92 -> 41159d5e",
+        "41186774 41268957 410ece6a 3f410c4e -> 41186774",
+        "410eaed8 411d04de 410810c1 3f27a0ea -> 410eaed8",
+        "40828f6a 409a1424 406f7342 3f5e3057 -> 4082d395",
+        "4115be3f 4120deab 41116cb9 3ef71f23 -> 4115be3f",
+        "406b6a82 408bd5ec 40300634 3f6d913a -> 406b6a82",
+        "40aaefac 40b38fff 4091e7a0 3f48405c -> 40aaefac",
+        "409e906a 40ab871a 409da159 3e5e5c0f -> 409e906a",
+        "409ba26f 40bd329a 4095f4c9 3f1cf745 -> 409ba26f",
+        "400f19f3 4057d6ac 3ff4d59d 3f3ad7bb -> 400f19f3",
+        "3ede1db2 3f789854 3d2e866e 3eedafed -> 3ede1db2",
+        "4116a22d 411cb325 41165124 3e4c4011 -> 4116a22d",
+        "40b275bf 40b2e530 40b253ff 3bcd5e11 -> 40b275bf",
+        "40ca1a46 40db2367 40ca0718 3e87e630 -> 40ca1a46",
+        "40bca173 40f119db 40ba564e 3f5b0e34 -> 40bca173",
+        "412142c2 413bf83d 411b7dc2 3f3e2241 -> 412142c2",
+        "411996d5 412f673a 4116e1e8 3ea9d110 -> 411996d5",
+        "3fed60f0 404c2b7b 3fbd0da7 3f3504cb -> 3fed60f0",
+        "40d48552 40edeb28 40b53af5 3f7a52ec -> 40d48552",
+        "3f1020c4 3fdaa14b 3ef93a2c 3e002863 -> 3f1020c4",
+        "40f98c05 4108d4dd 40eabb1a 3efbb972 -> 40f98c05",
+        "3fe99b2a 4014edf8 3fdd9842 3e98875c -> 3fe99b2a",
+        "3f34d106 3ed71de9 3de5dc54 3f574138 -> 3ee539eb",
+        "406dd12b 408085c4 40699828 3f0de8fc -> 406ed757",
+        "40814882 40b70758 406c490a 3f800000 -> 40814882",
+        "412268da 413e2f40 411e2f40 3f800000 -> 412268da",
+        "400f2f74 4081e894 4003d127 3f800000 -> 400f2f74",
+        "41078b27 410b6b41 40fde4e9 3f098b2e -> 41078b27"
+      ]
+    },
+    {
+      "glsl": "vec4 cultmath_power_border(vec3, vec4[128], int)",
+      "tolerance": "ulp-bounded",
+      "cases": [
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       ]
     }
   ]

From a88df479b849ba4bec1345cab9bde96093002f17 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:23:43 +0200
Subject: [PATCH 06/21] cultmath_weighted_lattice_cells: the ring exit takes
 (float)(k - 1), GLSL ES has no int-to-float promotion

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/shaders/CultMath.hlsl                         | 2 +-
 .../cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl  | 2 +-
 2 files changed, 2 insertions(+), 2 deletions(-)

diff --git a/packages/cultmath/shaders/CultMath.hlsl b/packages/cultmath/shaders/CultMath.hlsl
index 480074f2..9c1b3307 100644
--- a/packages/cultmath/shaders/CultMath.hlsl
+++ b/packages/cultmath/shaders/CultMath.hlsl
@@ -772,7 +772,7 @@ float4 cultmath_weighted_lattice_cells(float2 p, float time, float4 bodies[CULTM
     int reach = 0;
     for (int k = 0; k <= 37; k++)
     {
-        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+        if (k > 1 && 0.5 * (float)(k - 1) >= max(f2, f1 + 2.0 * smoothing))
             break;
         for (int dz = -k; dz <= k; dz++)
         {
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
index 480074f2..9c1b3307 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
+++ b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
@@ -772,7 +772,7 @@ float4 cultmath_weighted_lattice_cells(float2 p, float time, float4 bodies[CULTM
     int reach = 0;
     for (int k = 0; k <= 37; k++)
     {
-        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+        if (k > 1 && 0.5 * (float)(k - 1) >= max(f2, f1 + 2.0 * smoothing))
             break;
         for (int dz = -k; dz <= k; dz++)
         {

From 773a3efbc9443d9fa484207af7985285a449eb0b Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:26:03 +0200
Subject: [PATCH 07/21] CultMath: regenerate the GLSL and re-record the
 lavapipe bounds on Yggdrasil for the site-array families

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/shaders/CultMath.glsl       |  2 +-
 .../fixtures/device-bounds-lavapipe.txt       | 44 ++++++++++---------
 2 files changed, 25 insertions(+), 21 deletions(-)

diff --git a/packages/cultmath/shaders/CultMath.glsl b/packages/cultmath/shaders/CultMath.glsl
index 32318111..bc62c0c1 100644
--- a/packages/cultmath/shaders/CultMath.glsl
+++ b/packages/cultmath/shaders/CultMath.glsl
@@ -772,7 +772,7 @@ vec4 cultmath_weighted_lattice_cells(vec2 p, float time, vec4 bodies[CULTMATH_MA
     int reach = 0;
     for (int k = 0; k <= 37; k++)
     {
-        if (k > 1 && 0.5 * (k - 1) >= max(f2, f1 + 2.0 * smoothing))
+        if (k > 1 && 0.5 * float(k - 1) >= max(f2, f1 + 2.0 * smoothing))
             break;
         for (int dz = -k; dz <= k; dz++)
         {
diff --git a/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt b/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
index b108aa4a..8764d2a4 100644
--- a/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
+++ b/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
@@ -20,14 +20,14 @@ lavapipe-glsl	15	vec2 cultmath_iv_min(vec2, vec2)	ulp-bounded	256	0	0	a324b35cb4
 lavapipe-glsl	16	vec2 cultmath_iv_max(vec2, vec2)	ulp-bounded	256	0	0	d68412262ca234c1da130fc5217ba6856da3e92e435c28c1fbdbf3692a89e1fa
 lavapipe-glsl	17	vec2 cultmath_iv_sqr(vec2)	ulp-bounded	256	0	0	dbbb0e0df015456393452377d689732428a9a8e24d8e2b407ee9620593b4c46b
 lavapipe-glsl	18	vec2 cultmath_iv_sqrt(vec2)	ulp-bounded	256	0	0	95bd15d1b283713fc632ced350f5da1b89f8f73e6618329773db1b52acd29991
-lavapipe-glsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	268d61fd6d122e2b85e211c96daf410fb7e2d8ff83ec2082709f640504c852a7
+lavapipe-glsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	abe9daf24930a5e3a49ec994c4cae3a0c27b9d019d6d93ec1963ec3daad664a0
 lavapipe-glsl	20	vec2 cultmath_iv_saturate(vec2)	ulp-bounded	256	0	0	0f844ef8c4d9a9f748c80677bbbfc36b5f6e682eb87c2d46e7e20635d5f55c26
 lavapipe-glsl	21	vec2 cultmath_iv_smoothstep(float, float, vec2)	ulp-bounded	256	0	0	3d5944a4c43feb91d6786924e0f5439c05285d28ff1f500b5582893758dd4ce5
 lavapipe-glsl	22	vec2 cultmath_iv_lerp(vec2, vec2, float)	ulp-bounded	256	0	0	96b09e90a3fbbfe81379a29a23b676e490bc7dc6bb731450197707e6cf4c573f
 lavapipe-glsl	23	vec2 cultmath_iv_snoise_ball(vec3, float)	ulp-bounded	242	54	0	570eb031260c8f4aab42edc57a5fa1d0da70e8a4e6f0b4bf68208c15506f7cb5
 lavapipe-glsl	24	vec2 cultmath_iv_fbm_ball(vec3, float, int, float, float)	ulp-bounded	250	56	0	9e7017426314537f84c58dcdd1f85188cbe8f4dd9ababed887f60776cf861ebf
 lavapipe-glsl	25	vec4 cultmath_iv_frustum_ball(vec2, float, float, float, float)	ulp-bounded	198	1.6457063576593662	0	327c306aa4d06aecbb2681d8808c6dbf0567e87b54a6067c68001e36b3e52169
-lavapipe-glsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	1a46b0fa116f55e5abd70ec9f2a66de0befe8b3577fe472f9eaa98932aae8040
+lavapipe-glsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	b4af8232dc3dd782cc6d790e928ede0f6ba6dfdffd6c71dd9494fb58973e485c
 lavapipe-glsl	27	CultPhasor cultmath_phacelle(vec3, vec3, float, float)	ulp-bounded, platform exp, sin, cos; across platforms |diff| <= 2^-20 max(|v|, 1); on a device |diff| <= 2^-18 max(|v|, 1)	0	18.5	0	705b4c18027a0838218645e9368c3749ae4b5bf75e0485985725e8e72b73ab88
 lavapipe-glsl	28	float cultmath_snoise(vec3)	ulp-bounded, on the simplex tie set	127	112	0	6929326e4f27726d7bbdbac3a7823209e2ecfcd301018ef164527c4c1a9f7ae8
 lavapipe-glsl	29	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, on the simplex tie set	102	546.5	0	6173a812fd4059fa19bce84d34858c6035cdda98aa21a2b210e611cbd58c29d6
@@ -36,7 +36,7 @@ lavapipe-glsl	31	vec3 cultmath_af_symbol(float, float)	ulp-bounded	256	0	0	04147
 lavapipe-glsl	32	vec3 cultmath_af_from_iv(vec2)	ulp-bounded	256	0	0	306fe58a3268199fc8fd845a32d956f349a790422fa5c87d5a0824636cb55424
 lavapipe-glsl	33	vec2 cultmath_af_range(vec3)	ulp-bounded	256	0	0	6245eeba19473d69d0d8155e20e2e6089a6843140723d23ed5d501064023a44a
 lavapipe-glsl	34	vec3 cultmath_af_add(vec3, vec3)	ulp-bounded	256	0	0	cb1cb3fc69224837342de767525d332687b9d3e17b3de255c28e2f0f65f32640
-lavapipe-glsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	df44c501a8be20dc46a54faac9583da13f4367adc501a33fe14624f10e54b558
+lavapipe-glsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	a8fad8ea86cf61841430293fdd9840a54008160250114040380c9634c63bb17e
 lavapipe-glsl	36	vec3 cultmath_af_neg(vec3)	ulp-bounded	256	0	0	e485acf8ee21c6d880621cc6216b3b2a78318f56f5864b33c5509be27e22a694
 lavapipe-glsl	37	vec3 cultmath_af_scale(vec3, float)	ulp-bounded	256	0	0	8b0c8a540fea82fe058efc42ffa38dbd69850e579cefe5fdbc4c164b715ec15d
 lavapipe-glsl	38	vec3 cultmath_af_add_iv(vec3, vec2)	ulp-bounded	256	0	0	620f747e6ba53014c9714a8dbfaa3ff93f281c80938bd035ef64657e3bdc1a16
@@ -50,7 +50,7 @@ lavapipe-glsl	45	vec3 cultmath_af_snoise(vec3, vec3, float)	ulp-bounded, reach 1
 lavapipe-glsl	46	vec3 cultmath_af_fbm(vec3, vec3, float, int, float, float)	ulp-bounded, reach 1e-6 to 1e-3	27	102.5	0	42246db4e19a1da20433517cdc7016dda375ea70dc90d1a777679bfd76fb59e8
 lavapipe-glsl	47	float cultmath_cycles_divide(float, float)	ulp-bounded	256	0	0	87f143c57806ad52c3295cde67e97f31e39c8572b8c0a4b8c577e6fcd8ecbebf
 lavapipe-glsl	48	float cultmath_cycles_power(float, float)	ulp-bounded, platform pow	136	4.918926113980705	0	0e62db5ea32fdb9fdd3a9b135a914ddadd3231bdee0ff15c709102b26bb89186
-lavapipe-glsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	147	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
+lavapipe-glsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	146	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
 lavapipe-glsl	50	float cultmath_cycles_sqrt(float)	ulp-bounded	256	0	0	6d4beb34e93ae304b3d9d30f203fb6c2ba222affc0efc35bb5441528e9062a9a
 lavapipe-glsl	51	float cultmath_cycles_inverse_sqrt(float)	ulp-bounded	256	0	0	71aadd5bd384b9ca2eb89827de53af810a1350b02177de1987e9405e4a6e9ad8
 lavapipe-glsl	52	float cultmath_cycles_modulo(float, float)	ulp-bounded	256	0	0	cf055cafcb5b2d4789a0a2d5cfbc8bc79f52df646b60f5e47db3f994680949e9
@@ -96,16 +96,16 @@ lavapipe-glsl	91	vec3 cultmath_cycles_mix_val(float, vec3, vec3)	ulp-bounded	256
 lavapipe-glsl	92	vec3 cultmath_cycles_mix_color(float, vec3, vec3)	ulp-bounded	256	0	0	00067b1567bcd6c07a81fa5002f145dfca22437a3f3df5389b2665334d14909b
 lavapipe-glsl	93	vec3 cultmath_cycles_mix_soft(float, vec3, vec3)	ulp-bounded	157	1.9750388068880254	0	ed7c5508ca0543cc20a5f0c5624e75e3ca2a2d6044d481816eeda2edc50c0592
 lavapipe-glsl	94	vec3 cultmath_cycles_mix_linear(float, vec3, vec3)	ulp-bounded	256	0	0	672435cc30bcbbb253cce7316ee0712b1a18f06924bc89cea2d3388dd164a15d
-lavapipe-glsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	155	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
+lavapipe-glsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	154	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
 lavapipe-glsl	96	float cultmath_cycles_arccosine(float)	ulp-bounded, platform acos	79	1046.8674409774287	0	22a2c38ab5a232cdbb33cf0c133362581a398f64a4d0d5d6dd89dc5af06bd890
-lavapipe-glsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	7	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
+lavapipe-glsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	6	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
 lavapipe-glsl	98	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded	30	1358.4375	0	62bbafb8420ed5aaa0ce11d1470ca98945e690b186c33a1e7cf4d71478396465
 lavapipe-glsl	99	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, on the simplex tie set	110	1317.4754224467295	0	0efd9b3a637b46033ed0351f64de274db4d9ce05bb83dd1ce57afb3ceaea26bc
 lavapipe-glsl	100	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded	256	0	0	84bf9c9a2126b3114a692507cc54f58d313afc33de8a1cac83969cc508433cbe
 lavapipe-glsl	101	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, lo above hi and infinite bounds	256	0	0	ff999094d7794aa525e0f9f9a067aa21408a59559aa546cace3b1bb4a8c7f96d
 lavapipe-glsl	102	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, zero-length spans and flat infinite clamps	256	0	0	c3cc48f4edcac6801b9223f12d289934916431bdfaea8f68af33a1b833ab9860
 lavapipe-glsl	103	SpanNoise cultmath_span_fbm(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	1012477.3459086476	0	97c531c3a690e056d95e949e243ae74111d4a93a39fd22c0358a103b3bb14bc1
-lavapipe-glsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	8	948534.9108393334	0	c5d55a1d05403f6a1a7b7946c3a4c9556277f217fc660d338b3894efbb333e43
+lavapipe-glsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	8	948534.9108393334	0	54fd229d69439ff3318690b7802143f8410dc7ece30ad0d56ccc4b68bf39bec2
 lavapipe-glsl	105	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	116	249.5	0	fff9658a8ec055766c9327ee9b680cf7fb83736c472ae90a11e50d6d2a053fdc
 lavapipe-glsl	106	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e2 to 4e6	70	11866336.625	0	833484714ebcea59d86e0fbc2eaa4ae247c29541703763989e6758547dbf6db8
 lavapipe-glsl	107	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	120	980.7417469278579	0	3ea43dabe0091ea8e994c1dfc65c7274ed38b9343d4d1d06f7caa09c806c91df
@@ -117,13 +117,15 @@ lavapipe-glsl	112	vec3 cultmath_segment_closest(vec3, vec3, vec3)	ulp-bounded	21
 lavapipe-glsl	113	vec4 cultmath_power_border_step(vec3, vec4, vec4, vec4)	ulp-bounded	214	43	0	fdfdff73434a146489b002af5e80663658b2dd7b86105a7e65bdab755ab54a5e
 lavapipe-glsl	114	vec4 cultmath_power_score(vec3, vec4)	ulp-bounded	207	1.4619722193127032	0	dc1aa639ae1dc44003a0f5d8c7c99b2e3d7f51b158c96b3c3bd7a9f7df6d927e
 lavapipe-glsl	115	vec4 cultmath_multiplicative_score(vec3, vec4)	ulp-bounded	234	1.5529504197086745	0	ee1af26ac82489e8d363e7a6b6b59da7dacfb397d4bc9a723dd68607a69da41a
-lavapipe-glsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	b8687b139aaa865e9f28fbc84fe37dd4a1d4873d5ff8e2074922c07f56551576
+lavapipe-glsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	bfad8b369011cfbf14644fec68ce65620694fcbf3cd3804f54953d55587313fc
 lavapipe-glsl	117	vec4 cultmath_site_cells_border(CultSiteCells)	ulp-bounded	228	1.069496760346883	0	d7b478bef7e6f80902d0b5b255cb4fca30757ff6b9d25dac2030b037a8d342ce
 lavapipe-glsl	118	float cultmath_gabriel_margin(vec3, vec3, vec3)	ulp-bounded	201	2	0	6a80fbef486de496a08b7c8e7f9f65e2cc0f5b9f93abe50c43e84ad88d1ed034
 lavapipe-glsl	119	vec3 cultmath_lattice_site(vec2, float, float)	ulp-bounded	256	0	0	84df739c336796638dcf0a99c328a4b8c150c25d80e02248d4b6d023dc13161f
 lavapipe-glsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-bounded	231	2.0671110200639147	0	434cdf5603abc2942aa624b9d2e98d5f1231706c86180a80439bc8b72bdd066e
-lavapipe-glsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	622d0e1ea0fcf0e2700558dbdaea92b8ce02e44048dbf35944c23b5088c3e40c
-lavapipe-glsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	e6c9aeb52c5e63ebf3c8525dd39b5b88d5f890fd4f23f4894a92232807a3d94e
+lavapipe-glsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	ba3fa3bdb4f5f5b2478a4ddfb2e08f2f425e997778a716884e43b13d6ed050b5
+lavapipe-glsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	6cbeddde536b12e83873f2e5ac60d16bef22049d2a7dea61af0ff1e0d5b84740
+lavapipe-glsl	123	vec4 cultmath_power_border(vec3, vec4[128], int)	ulp-bounded	188	65.72121683891783	0	8427c2b99109a4f59ff745fdb87f261deb1cbae34ce99bc1ae05ebb7f9963b4d
+lavapipe-glsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	192	2.5	0	a33083016b0018fe7f953058a401b1498e5b11d71f6e90336c529e0603857ef9
 lavapipe-hlsl	0	float cultmath_snoise(vec3)	ulp-bounded	94	122.6875	0	5d41c14241a13124f2e1b49f230f5df0c48d0d69fb1be9ef2f33dc1702bf0b0a
 lavapipe-hlsl	1	float cultmath_snoise(vec2)	ulp-bounded	204	1	0	81d9c62726afdccbbe4ffef173b5c92731eb6bf5927b3979d653e50dbd5d4064
 lavapipe-hlsl	2	vec4 cultmath_snoise_grad(vec3)	ulp-bounded	71	617.5	0	f7e9ed1707cdb015efaba0e0150193309da0d4c125349518f8b7c60a17b25790
@@ -143,14 +145,14 @@ lavapipe-hlsl	15	vec2 cultmath_iv_min(vec2, vec2)	ulp-bounded	256	0	0	a324b35cb4
 lavapipe-hlsl	16	vec2 cultmath_iv_max(vec2, vec2)	ulp-bounded	256	0	0	d68412262ca234c1da130fc5217ba6856da3e92e435c28c1fbdbf3692a89e1fa
 lavapipe-hlsl	17	vec2 cultmath_iv_sqr(vec2)	ulp-bounded	256	0	0	dbbb0e0df015456393452377d689732428a9a8e24d8e2b407ee9620593b4c46b
 lavapipe-hlsl	18	vec2 cultmath_iv_sqrt(vec2)	ulp-bounded	256	0	0	95bd15d1b283713fc632ced350f5da1b89f8f73e6618329773db1b52acd29991
-lavapipe-hlsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	268d61fd6d122e2b85e211c96daf410fb7e2d8ff83ec2082709f640504c852a7
+lavapipe-hlsl	19	vec2 cultmath_iv_clamp(vec2, float, float)	ulp-bounded	256	0	0	abe9daf24930a5e3a49ec994c4cae3a0c27b9d019d6d93ec1963ec3daad664a0
 lavapipe-hlsl	20	vec2 cultmath_iv_saturate(vec2)	ulp-bounded	256	0	0	0f844ef8c4d9a9f748c80677bbbfc36b5f6e682eb87c2d46e7e20635d5f55c26
 lavapipe-hlsl	21	vec2 cultmath_iv_smoothstep(float, float, vec2)	ulp-bounded	256	0	0	3d5944a4c43feb91d6786924e0f5439c05285d28ff1f500b5582893758dd4ce5
 lavapipe-hlsl	22	vec2 cultmath_iv_lerp(vec2, vec2, float)	ulp-bounded	256	0	0	96b09e90a3fbbfe81379a29a23b676e490bc7dc6bb731450197707e6cf4c573f
 lavapipe-hlsl	23	vec2 cultmath_iv_snoise_ball(vec3, float)	ulp-bounded	244	54	0	f36530a4cd8c9fdc1c73e7ddb6782cd11cbf8493e2ee7b0656e818812504267e
 lavapipe-hlsl	24	vec2 cultmath_iv_fbm_ball(vec3, float, int, float, float)	ulp-bounded	252	75	0	a1677ea42ce91a5d2b6f83fa7c44879b7a184ed4631108d7a1c6e710bf26ff02
 lavapipe-hlsl	25	vec4 cultmath_iv_frustum_ball(vec2, float, float, float, float)	ulp-bounded	198	1.6457063576593662	0	327c306aa4d06aecbb2681d8808c6dbf0567e87b54a6067c68001e36b3e52169
-lavapipe-hlsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	1a46b0fa116f55e5abd70ec9f2a66de0befe8b3577fe472f9eaa98932aae8040
+lavapipe-hlsl	26	vec2 cultmath_iv_exp(vec2)	ulp-bounded, platform exp	7	7.526057804152758	0	b4af8232dc3dd782cc6d790e928ede0f6ba6dfdffd6c71dd9494fb58973e485c
 lavapipe-hlsl	27	CultPhasor cultmath_phacelle(vec3, vec3, float, float)	ulp-bounded, platform exp, sin, cos; across platforms |diff| <= 2^-20 max(|v|, 1); on a device |diff| <= 2^-18 max(|v|, 1)	0	18.5	0	705b4c18027a0838218645e9368c3749ae4b5bf75e0485985725e8e72b73ab88
 lavapipe-hlsl	28	float cultmath_snoise(vec3)	ulp-bounded, on the simplex tie set	144	99	0	be76512b18eb678194dad0c4726c0aef9ba34012b60b79d24c2df27989707145
 lavapipe-hlsl	29	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, on the simplex tie set	111	546.5	0	124d4be07cbb66edab644e649c081cb7c8be5d99b6c1d84fec5d7ef65c76ed0f
@@ -159,7 +161,7 @@ lavapipe-hlsl	31	vec3 cultmath_af_symbol(float, float)	ulp-bounded	256	0	0	04147
 lavapipe-hlsl	32	vec3 cultmath_af_from_iv(vec2)	ulp-bounded	256	0	0	306fe58a3268199fc8fd845a32d956f349a790422fa5c87d5a0824636cb55424
 lavapipe-hlsl	33	vec2 cultmath_af_range(vec3)	ulp-bounded	256	0	0	6245eeba19473d69d0d8155e20e2e6089a6843140723d23ed5d501064023a44a
 lavapipe-hlsl	34	vec3 cultmath_af_add(vec3, vec3)	ulp-bounded	256	0	0	cb1cb3fc69224837342de767525d332687b9d3e17b3de255c28e2f0f65f32640
-lavapipe-hlsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	df44c501a8be20dc46a54faac9583da13f4367adc501a33fe14624f10e54b558
+lavapipe-hlsl	35	vec3 cultmath_af_sub(vec3, vec3)	ulp-bounded	256	0	0	a8fad8ea86cf61841430293fdd9840a54008160250114040380c9634c63bb17e
 lavapipe-hlsl	36	vec3 cultmath_af_neg(vec3)	ulp-bounded	256	0	0	e485acf8ee21c6d880621cc6216b3b2a78318f56f5864b33c5509be27e22a694
 lavapipe-hlsl	37	vec3 cultmath_af_scale(vec3, float)	ulp-bounded	256	0	0	8b0c8a540fea82fe058efc42ffa38dbd69850e579cefe5fdbc4c164b715ec15d
 lavapipe-hlsl	38	vec3 cultmath_af_add_iv(vec3, vec2)	ulp-bounded	256	0	0	620f747e6ba53014c9714a8dbfaa3ff93f281c80938bd035ef64657e3bdc1a16
@@ -173,7 +175,7 @@ lavapipe-hlsl	45	vec3 cultmath_af_snoise(vec3, vec3, float)	ulp-bounded, reach 1
 lavapipe-hlsl	46	vec3 cultmath_af_fbm(vec3, vec3, float, int, float, float)	ulp-bounded, reach 1e-6 to 1e-3	24	122.75	0	7f941b1f0c76d9f2121027a555ae7f2a741cc164402f0df75237198ac97f850b
 lavapipe-hlsl	47	float cultmath_cycles_divide(float, float)	ulp-bounded	256	0	0	87f143c57806ad52c3295cde67e97f31e39c8572b8c0a4b8c577e6fcd8ecbebf
 lavapipe-hlsl	48	float cultmath_cycles_power(float, float)	ulp-bounded, platform pow	136	4.918926113980705	0	0e62db5ea32fdb9fdd3a9b135a914ddadd3231bdee0ff15c709102b26bb89186
-lavapipe-hlsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	147	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
+lavapipe-hlsl	49	float cultmath_cycles_logarithm(float, float)	ulp-bounded, platform log	146	4.94622778071426	0	5b2bf1411512c7e5a3f4b335a16fc3ba00ba0784bb87acb14b7d1b9dd551b2f3
 lavapipe-hlsl	50	float cultmath_cycles_sqrt(float)	ulp-bounded	256	0	0	6d4beb34e93ae304b3d9d30f203fb6c2ba222affc0efc35bb5441528e9062a9a
 lavapipe-hlsl	51	float cultmath_cycles_inverse_sqrt(float)	ulp-bounded	256	0	0	71aadd5bd384b9ca2eb89827de53af810a1350b02177de1987e9405e4a6e9ad8
 lavapipe-hlsl	52	float cultmath_cycles_modulo(float, float)	ulp-bounded	256	0	0	cf055cafcb5b2d4789a0a2d5cfbc8bc79f52df646b60f5e47db3f994680949e9
@@ -219,16 +221,16 @@ lavapipe-hlsl	91	vec3 cultmath_cycles_mix_val(float, vec3, vec3)	ulp-bounded	256
 lavapipe-hlsl	92	vec3 cultmath_cycles_mix_color(float, vec3, vec3)	ulp-bounded	256	0	0	00067b1567bcd6c07a81fa5002f145dfca22437a3f3df5389b2665334d14909b
 lavapipe-hlsl	93	vec3 cultmath_cycles_mix_soft(float, vec3, vec3)	ulp-bounded	157	1.9750388068880254	0	ed7c5508ca0543cc20a5f0c5624e75e3ca2a2d6044d481816eeda2edc50c0592
 lavapipe-hlsl	94	vec3 cultmath_cycles_mix_linear(float, vec3, vec3)	ulp-bounded	256	0	0	672435cc30bcbbb253cce7316ee0712b1a18f06924bc89cea2d3388dd164a15d
-lavapipe-hlsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	155	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
+lavapipe-hlsl	95	float cultmath_cycles_arcsine(float)	ulp-bounded, platform asin	154	2734.286809678319	0	f28f3ed0a53ffeebdfa84865d2d3d41590e6b46fc1578d40e1215e2a9e1af585
 lavapipe-hlsl	96	float cultmath_cycles_arccosine(float)	ulp-bounded, platform acos	79	1046.8674409774287	0	22a2c38ab5a232cdbb33cf0c133362581a398f64a4d0d5d6dd89dc5af06bd890
-lavapipe-hlsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	7	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
+lavapipe-hlsl	97	float cultmath_cycles_arctan2(float, float)	ulp-bounded, platform atan	6	25.5	0	2c60447d80186f6dc9726f19c09fa96ec3f66d8f5688968da533d9195ea463c4
 lavapipe-hlsl	98	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded	33	2377.8799856935966	0	a64853839f394cc7c367ba5e107caa8bb396f07cf202263aa917095dd1c939f7
 lavapipe-hlsl	99	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, on the simplex tie set	132	1317.4754224467295	0	9066a49e50731881583ffca16c949171bb61578a1dfd497c54dafe773ab49488
 lavapipe-hlsl	100	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded	256	0	0	84bf9c9a2126b3114a692507cc54f58d313afc33de8a1cac83969cc508433cbe
 lavapipe-hlsl	101	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, lo above hi and infinite bounds	256	0	0	ff999094d7794aa525e0f9f9a067aa21408a59559aa546cace3b1bb4a8c7f96d
 lavapipe-hlsl	102	float cultmath_integral_clamp_linear(float, float, float, float, float, float)	ulp-bounded, zero-length spans and flat infinite clamps	256	0	0	c3cc48f4edcac6801b9223f12d289934916431bdfaea8f68af33a1b833ab9860
 lavapipe-hlsl	103	SpanNoise cultmath_span_fbm(SpanPath, SpanStage, int, float, float)	ulp-bounded	3	1024946.5723514018	0	f6395b9f2609d914894c35b442719be3cc3e11d07c5f0bae5a8719651e60cd4e
-lavapipe-hlsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	948534.9108393334	0	bfda3536007373bdbef75a5c7bb63a7192f1c90b082984588f23e5b4eb767867
+lavapipe-hlsl	104	SpanNoise cultmath_span_ridged(SpanPath, SpanStage, int, float, float)	ulp-bounded	7	948534.9108393334	0	2adfdc4e6c81ee0bc7bb7869c55207f5033b4176104bc36dce1528ae0a5fe39b
 lavapipe-hlsl	105	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	119	423.1430718408491	0	a94c38d1baa651a6faa510920cbe9d1f9528c0adb863ba6e35d835588ad00a58
 lavapipe-hlsl	106	vec4 cultmath_snoise_grad(vec3)	ulp-bounded, coordinate bands 1e2 to 4e6	73	13116827.1875	0	9ad0fd577b26aa717534c0693df97ee41bcded0768f442739b98f505e4a2a430
 lavapipe-hlsl	107	mat3 cultmath_snoise_hessian(vec3)	ulp-bounded, coordinate bands 1e-4 to 1e2	122	980.7417469278579	0	0977fa6f446e4f916a9b938ce24ea32df6aa912dc991c182014d309dc0efb1cb
@@ -240,10 +242,12 @@ lavapipe-hlsl	112	vec3 cultmath_segment_closest(vec3, vec3, vec3)	ulp-bounded	21
 lavapipe-hlsl	113	vec4 cultmath_power_border_step(vec3, vec4, vec4, vec4)	ulp-bounded	214	43	0	fdfdff73434a146489b002af5e80663658b2dd7b86105a7e65bdab755ab54a5e
 lavapipe-hlsl	114	vec4 cultmath_power_score(vec3, vec4)	ulp-bounded	207	1.4619722193127032	0	dc1aa639ae1dc44003a0f5d8c7c99b2e3d7f51b158c96b3c3bd7a9f7df6d927e
 lavapipe-hlsl	115	vec4 cultmath_multiplicative_score(vec3, vec4)	ulp-bounded	234	1.5529504197086745	0	ee1af26ac82489e8d363e7a6b6b59da7dacfb397d4bc9a723dd68607a69da41a
-lavapipe-hlsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	b8687b139aaa865e9f28fbc84fe37dd4a1d4873d5ff8e2074922c07f56551576
+lavapipe-hlsl	116	CultSiteCells cultmath_site_cells_insert(CultSiteCells, vec4, int)	ulp-bounded	256	0	0	bfad8b369011cfbf14644fec68ce65620694fcbf3cd3804f54953d55587313fc
 lavapipe-hlsl	117	vec4 cultmath_site_cells_border(CultSiteCells)	ulp-bounded	228	1.069496760346883	0	d7b478bef7e6f80902d0b5b255cb4fca30757ff6b9d25dac2030b037a8d342ce
 lavapipe-hlsl	118	float cultmath_gabriel_margin(vec3, vec3, vec3)	ulp-bounded	201	2	0	6a80fbef486de496a08b7c8e7f9f65e2cc0f5b9f93abe50c43e84ad88d1ed034
 lavapipe-hlsl	119	vec3 cultmath_lattice_site(vec2, float, float)	ulp-bounded	256	0	0	84df739c336796638dcf0a99c328a4b8c150c25d80e02248d4b6d023dc13161f
 lavapipe-hlsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-bounded	231	2.0671110200639147	0	434cdf5603abc2942aa624b9d2e98d5f1231706c86180a80439bc8b72bdd066e
-lavapipe-hlsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	622d0e1ea0fcf0e2700558dbdaea92b8ce02e44048dbf35944c23b5088c3e40c
-lavapipe-hlsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	e6c9aeb52c5e63ebf3c8525dd39b5b88d5f890fd4f23f4894a92232807a3d94e
+lavapipe-hlsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	ba3fa3bdb4f5f5b2478a4ddfb2e08f2f425e997778a716884e43b13d6ed050b5
+lavapipe-hlsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	6cbeddde536b12e83873f2e5ac60d16bef22049d2a7dea61af0ff1e0d5b84740
+lavapipe-hlsl	123	vec4 cultmath_power_border(vec3, vec4[128], int)	ulp-bounded	188	65.72121683891783	0	8427c2b99109a4f59ff745fdb87f261deb1cbae34ce99bc1ae05ebb7f9963b4d
+lavapipe-hlsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	192	2.5	0	a33083016b0018fe7f953058a401b1498e5b11d71f6e90336c529e0603857ef9

From 70914d9a952342c2083550dd0fb6fd5a46a350c7 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:30:19 +0200
Subject: [PATCH 08/21] CultMath: the fixture cases separate each lattice-loop
 mutant from the shader text

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 .../CultMath.Tests/GlslMirrorTests.Mutants.cs | 59 +++++++++++++++++++
 .../HlslSourceCompatibilityTests.cs           |  4 +-
 2 files changed, 62 insertions(+), 1 deletion(-)
 create mode 100644 packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs

diff --git a/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs
new file mode 100644
index 00000000..a9701838
--- /dev/null
+++ b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs
@@ -0,0 +1,59 @@
+using System.Reflection;
+using System.Text.RegularExpressions;
+using Xunit;
+
+namespace CultMath.Tests;
+
+public sealed partial class GlslMirrorTests
+{
+    private const string Weighted = "cultmath_weighted_lattice_cells(";
+    private const string SmoothStep = "cultmath_lattice_smooth_step(";
+
+    // Edits of the shader text that each break one rule of the lattice loop. M7 (the exit one ring late) is absent: by the
+    // window-independence proof a later exit visits more cells and changes nothing, so no case can kill it.
+    private static readonly (string Name, string Function, string Old, string New, int Kills)[] LatticeMutants =
+    {
+        ("M1 exit one ring early", Weighted, "0.5 * (float)(k - 1) >= max(f2", "0.5 * (float)k >= max(f2", 3),
+        ("M2 exit ignores the smoothing band", Weighted, ">= max(f2, f1 + 2.0 * smoothing))", ">= f2)", 1),
+        ("M3 no pre-normalisation of the normal", Weighted, "normal = stretchNormal / scale;", "normal = stretchNormal;", 1),
+        ("M4 no unit length for the normal", Weighted, "normal = normal / length(normal);", "normal = normal * 1.0;", 1),
+        ("M5 smooth step without its clamp", SmoothStep, "return min(next, f1 + smoothing);", "return next;", 1),
+        ("M6 box pass skips its first row", Weighted, "for (int dz = -reach; dz <= reach; dz++)", "for (int dz = -reach + 1; dz <= reach; dz++)", 1),
+    };
+
+    /// <summary>
+    /// Each rule of the lattice loop is pinned by the committed fixture's own cases: the shader text with one rule broken (a
+    /// mutant mirror, the text a device runs) returns another result than the fixture on at least the stated number of
+    /// cases of the family that exercises it, the exit one ring early on at least three. The device judge holds the same
+    /// cases to their recorded bound, so a mutant these cases separate fails it too.
+    /// </summary>
+    [Fact]
+    public void TheFixtureCasesSeparateEveryLatticeMutantFromTheShader()
+    {
+        var families = FixtureFamilies();
+        foreach (var (name, function, old, replacement, kills) in LatticeMutants)
+        {
+            var (assembly, errors) = HlslSourceCompatibilityTests.CompileShaderMirror(mutate: text =>
+            {
+                Assert.True(text.Split(old).Length == 2, $"{name}: the shader text no longer holds exactly one \"{old}\"");
+                return text.Replace(old, replacement);
+            });
+            Assert.True(assembly is not null, name + ": " + string.Join(Environment.NewLine, errors));
+            var shaderType = assembly!.GetType("CultMathHlsl.HlslShader")!;
+            var shader = Activator.CreateInstance(shaderType);
+            var mirror = shaderType.GetMethod(function[..^1], BindingFlags.Instance | BindingFlags.NonPublic)!;
+
+            var f = Array.FindIndex(Families, family => family.Glsl.Contains(function));
+            var method = Resolve(Families[f].Glsl);
+            var killed = 0;
+            foreach (var entry in families[f]!["cases"]!.AsArray())
+            {
+                var sides = Sides(entry);
+                if (Hex(new[] { mirror.Invoke(shader, Arguments(method, sides[0]))! }) != sides[1])
+                    killed++;
+            }
+
+            Assert.True(killed >= kills, $"{name}: the {Families[f].Glsl} fixture cases separate it on {killed} of {Points}, fewer than {kills}");
+        }
+    }
+}
diff --git a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
index 41770546..2c994be8 100644
--- a/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/HlslSourceCompatibilityTests.cs
@@ -782,9 +782,11 @@ public sealed class HlslSourceCompatibilityTests
         return "using CultMath;\nusing static CultMath.math;\nnamespace CultMathHlsl;\npublic class HlslShader\n{\n" + members + source + "\n}\n";
     }
 
-    internal static (Assembly? Assembly, IReadOnlyList<string> Errors) CompileShaderMirror(string members = "", IReadOnlyDictionary<string, int>? defines = null)
+    internal static (Assembly? Assembly, IReadOnlyList<string> Errors) CompileShaderMirror(string members = "", IReadOnlyDictionary<string, int>? defines = null, Func<string, string>? mutate = null)
     {
         var hlsl = ReadShaderSource(FindCultMathRoot());
+        if (mutate is not null)
+            hlsl = mutate(hlsl);
         var tree = CSharpSyntaxTree.ParseText(TransformHlslToCSharp(hlsl, members, defines));
         var references = ((string)AppContext.GetData("TRUSTED_PLATFORM_ASSEMBLIES")!)
             .Split(Path.PathSeparator)

From ce6e39a28225faa51acc530e2626822803187106 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:46:17 +0200
Subject: [PATCH 09/21] SiteArrays: ExitBoundPoints, lattice draws where an
 exit one ring early reads another result

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 .../tests/CultMath.Tests/LatticeCellsTests.cs |  4 +-
 .../tests/CultMath.Tests/SiteArrays.cs        | 37 +++++++++++++++++--
 2 files changed, 36 insertions(+), 5 deletions(-)

diff --git a/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs b/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
index 22de49c8..f6363da1 100644
--- a/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/LatticeCellsTests.cs
@@ -41,7 +41,7 @@ public sealed class LatticeCellsTests
     }
 
     // Folds F1, F2, id and smooth over the box of the given radius in absolute row-major order.
-    private static float4 BoxFold(float2 p, float time, float4[] bodies, Look look, int radius,
+    internal static float4 BoxFold(float2 p, float time, float4[] bodies, Look look, int radius,
         Dictionary<(int, int), float> weights, float2? unitNormal = null)
     {
         var q = p / Cell;
@@ -71,7 +71,7 @@ public sealed class LatticeCellsTests
         return new float4(f1, f2, m, cellular_unit(id.w));
     }
 
-    private static float4 Call(float2 p, float time, float4[] bodies, Look look, float2? normal = null) =>
+    internal static float4 Call(float2 p, float time, float4[] bodies, Look look, float2? normal = null) =>
         weighted_lattice_cells(p, time, bodies, Cell, Drift, look.Boost, look.Falloff, look.Smoothing, normal ?? Normal, look.Stretch);
 
     internal static float2 RandomPoint(System.Random r) =>
diff --git a/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
index cc3a4bf8..b656a874 100644
--- a/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
+++ b/packages/cultmath/tests/CultMath.Tests/SiteArrays.cs
@@ -108,12 +108,43 @@ internal static class SiteArrays
         return found;
     }
 
+    /// <summary>
+    /// Points where an exit one ring early (the rule "bound 0.5*k") returns another result than the exact search, found once by
+    /// running both on the six orbiting bodies under each look: the cases that pin the ring exit to the bit.
+    /// </summary>
+    internal static readonly IReadOnlyList<(float2 P, float Time, LatticeCellsTests.Look Look)> ExitBoundPoints = FindExitBoundPoints();
+
+    private static List<(float2, float, LatticeCellsTests.Look)> FindExitBoundPoints()
+    {
+        var found = new List<(float2, float, LatticeCellsTests.Look)>();
+        var looks = LatticeCellsTests.Looks.Append(WidestLook).ToArray();
+        var r = new System.Random(0xE517);
+        while (found.Count < 24)
+        {
+            var p = LatticeCellsTests.RandomPoint(r);
+            var time = 13.0f * r.Next(20);
+            var look = looks[r.Next(looks.Length)];
+            var bodies = LatticeCellsTests.Bodies(time);
+            var early = LatticeCellsTests.Radius(p, time, bodies, look, LatticeCellsTests.Rules[2].stop, new Dictionary<(int, int), float>());
+            if (early >= LatticeCellsTests.Radius(p, time, bodies, look, LatticeCellsTests.Rules[0].stop, new Dictionary<(int, int), float>()))
+                continue;
+            if (!LatticeCellsTests.BoxFold(p, time, bodies, look, Math.Max(0, early), new Dictionary<(int, int), float>()).Equals(LatticeCellsTests.Call(p, time, bodies, look)))
+                found.Add((p, time, look));
+        }
+
+        return found;
+    }
+
     internal static object[] LatticeArguments(System.Random r)
     {
-        if (r.Next(3) == 0)
+        switch (r.Next(4))
         {
-            var far = FarPoints[r.Next(FarPoints.Count)];
-            return Lattice(far.P, far.Time, Padded(LatticeCellsTests.Bodies(far.Time)), 6, WidestLook, LatticeCellsTests.Normal);
+            case 0:
+                var far = FarPoints[r.Next(FarPoints.Count)];
+                return Lattice(far.P, far.Time, Padded(LatticeCellsTests.Bodies(far.Time)), 6, WidestLook, LatticeCellsTests.Normal);
+            case 1:
+                var tight = ExitBoundPoints[r.Next(ExitBoundPoints.Count)];
+                return Lattice(tight.P, tight.Time, Padded(LatticeCellsTests.Bodies(tight.Time)), 6, tight.Look, LatticeCellsTests.Normal);
         }
 
         var time = 13.0f * r.Next(20);

From 8a0b98f70f206ba8d56d362bab9fcb24c862a094 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:48:54 +0200
Subject: [PATCH 10/21] CultMath: re-record the fixture and lavapipe bounds on
 Yggdrasil after the exit-bound draws; the mutant test prints its kill counts

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 .../CultMath.Tests/GlslMirrorTests.Mutants.cs |   1 +
 .../fixtures/device-bounds-lavapipe.txt       |   4 +-
 .../CultMath.Tests/fixtures/glsl-parity.json  | 466 +++++++++---------
 3 files changed, 236 insertions(+), 235 deletions(-)

diff --git a/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs
index a9701838..c896a6a1 100644
--- a/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs
+++ b/packages/cultmath/tests/CultMath.Tests/GlslMirrorTests.Mutants.cs
@@ -53,6 +53,7 @@ public sealed partial class GlslMirrorTests
                     killed++;
             }
 
+            output.WriteLine($"{name}: separated on {killed} of {Points} cases of {Families[f].Glsl}");
             Assert.True(killed >= kills, $"{name}: the {Families[f].Glsl} fixture cases separate it on {killed} of {Points}, fewer than {kills}");
         }
     }
diff --git a/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt b/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
index 8764d2a4..42706157 100644
--- a/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
+++ b/packages/cultmath/tests/CultMath.Tests/fixtures/device-bounds-lavapipe.txt
@@ -125,7 +125,7 @@ lavapipe-glsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-
 lavapipe-glsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	ba3fa3bdb4f5f5b2478a4ddfb2e08f2f425e997778a716884e43b13d6ed050b5
 lavapipe-glsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	6cbeddde536b12e83873f2e5ac60d16bef22049d2a7dea61af0ff1e0d5b84740
 lavapipe-glsl	123	vec4 cultmath_power_border(vec3, vec4[128], int)	ulp-bounded	188	65.72121683891783	0	8427c2b99109a4f59ff745fdb87f261deb1cbae34ce99bc1ae05ebb7f9963b4d
-lavapipe-glsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	192	2.5	0	a33083016b0018fe7f953058a401b1498e5b11d71f6e90336c529e0603857ef9
+lavapipe-glsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	179	3	0	fd3b58c4e2ba8a7bf801a1e6cdff82468abcb368442bc98b2583fda9d2e6f823
 lavapipe-hlsl	0	float cultmath_snoise(vec3)	ulp-bounded	94	122.6875	0	5d41c14241a13124f2e1b49f230f5df0c48d0d69fb1be9ef2f33dc1702bf0b0a
 lavapipe-hlsl	1	float cultmath_snoise(vec2)	ulp-bounded	204	1	0	81d9c62726afdccbbe4ffef173b5c92731eb6bf5927b3979d653e50dbd5d4064
 lavapipe-hlsl	2	vec4 cultmath_snoise_grad(vec3)	ulp-bounded	71	617.5	0	f7e9ed1707cdb015efaba0e0150193309da0d4c125349518f8b7c60a17b25790
@@ -250,4 +250,4 @@ lavapipe-hlsl	120	float cultmath_lattice_weight(float, float, float, float)	ulp-
 lavapipe-hlsl	121	float cultmath_lattice_distance(vec2, vec2, float, vec2, float)	ulp-bounded	256	0	0	ba3fa3bdb4f5f5b2478a4ddfb2e08f2f425e997778a716884e43b13d6ed050b5
 lavapipe-hlsl	122	float cultmath_lattice_smooth_step(float, float, float, float)	ulp-bounded	256	0	0	6cbeddde536b12e83873f2e5ac60d16bef22049d2a7dea61af0ff1e0d5b84740
 lavapipe-hlsl	123	vec4 cultmath_power_border(vec3, vec4[128], int)	ulp-bounded	188	65.72121683891783	0	8427c2b99109a4f59ff745fdb87f261deb1cbae34ce99bc1ae05ebb7f9963b4d
-lavapipe-hlsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	192	2.5	0	a33083016b0018fe7f953058a401b1498e5b11d71f6e90336c529e0603857ef9
+lavapipe-hlsl	124	vec4 cultmath_weighted_lattice_cells(vec2, float, vec4[128], int, float, float, float, float, float, vec2, float)	ulp-bounded	179	3	0	fd3b58c4e2ba8a7bf801a1e6cdff82468abcb368442bc98b2583fda9d2e6f823
diff --git a/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json b/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
index 8f1fa987..f2ab1f19 100644
--- a/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
+++ b/packages/cultmath/tests/CultMath.Tests/fixtures/glsl-parity.json
@@ -32516,145 +32516,220 @@
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       ]
     }
   ]

From b6f61ea8c40c8b525832e80d29ac1349d5bdaa11 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:50:15 +0200
Subject: [PATCH 11/21] CultMath.hlsl: the capacity note names no resource type

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/docs/design.md                              | 4 ++--
 packages/cultmath/shaders/CultMath.hlsl                       | 2 +-
 .../unity/org.gamecult.cultmath/Shaders/CultMath.hlsl         | 2 +-
 3 files changed, 4 insertions(+), 4 deletions(-)

diff --git a/packages/cultmath/docs/design.md b/packages/cultmath/docs/design.md
index 4e55dae4..62c6ed00 100644
--- a/packages/cultmath/docs/design.md
+++ b/packages/cultmath/docs/design.md
@@ -572,8 +572,8 @@ A shader function cannot take a span, so `cultmath_power_border(p, sites, count)
 and `cultmath_weighted_lattice_cells(p, time, bodies, count, ...)` take `float4 sites[CULTMATH_MAX_SITES]` by value and the
 count in use, with `count` in `[0, CULTMATH_MAX_SITES]`. `CULTMATH_MAX_SITES` is 128 unless the consumer defines it before
 including the library (`#ifndef`): 128 covers every Aetheria zone within GLSL ES 3.00's 224 guaranteed fragment uniform
-vectors, and loops run to `count`, so the capacity costs uniform space, not iterations. A `StructuredBuffer` caller copies
-into a local array first; the library takes no resource, accessor macro or uniform of its own. The preconditions the C#
+vectors, and loops run to `count`, so the capacity costs uniform space, not iterations. A caller whose sites live in a
+buffer copies them into a local array first; the library takes no resource, accessor macro or uniform of its own. The preconditions the C#
 functions throw for are the caller's in a shader (finite arguments, `cellSize > 0`, the stated ranges, `p` within 2^23
 cells). The ring pass is bounded `k <= 37` and exits as C# does; the box pass recomputes each distance instead of caching
 75 x 75 of them, which gives the same values. The C# mirror compiles the array as `T[]`, and
diff --git a/packages/cultmath/shaders/CultMath.hlsl b/packages/cultmath/shaders/CultMath.hlsl
index 9c1b3307..d3eea396 100644
--- a/packages/cultmath/shaders/CultMath.hlsl
+++ b/packages/cultmath/shaders/CultMath.hlsl
@@ -721,7 +721,7 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
 
 // Sites by value: a shader function cannot take a span, so these take float4 sites[CULTMATH_MAX_SITES] and the count in use, with
 // count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
-// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// run to count, so the capacity costs uniform space, not iterations. A caller whose sites live in a buffer copies them into a local array first.
 // The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
 // falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
 // cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
index 9c1b3307..d3eea396 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
+++ b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.hlsl
@@ -721,7 +721,7 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
 
 // Sites by value: a shader function cannot take a span, so these take float4 sites[CULTMATH_MAX_SITES] and the count in use, with
 // count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
-// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// run to count, so the capacity costs uniform space, not iterations. A caller whose sites live in a buffer copies them into a local array first.
 // The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
 // falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
 // cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the

From 92d4d5eb71ba392781728a7cf534b81419e98a21 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 16:50:50 +0200
Subject: [PATCH 12/21] CultMath: regenerate CultMath.glsl on Yggdrasil after
 the capacity note

Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
---
 packages/cultmath/shaders/CultMath.glsl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/packages/cultmath/shaders/CultMath.glsl b/packages/cultmath/shaders/CultMath.glsl
index bc62c0c1..6ebf3f36 100644
--- a/packages/cultmath/shaders/CultMath.glsl
+++ b/packages/cultmath/shaders/CultMath.glsl
@@ -721,7 +721,7 @@ float cultmath_lattice_smooth_step(float m, float d, float f1, float smoothing)
 
 // Sites by value: a shader function cannot take a span, so these take vec4 sites[CULTMATH_MAX_SITES] and the count in use, with
 // count in [0, CULTMATH_MAX_SITES]. A consumer defines CULTMATH_MAX_SITES before including this file to change the capacity; loops
-// run to count, so the capacity costs uniform space, not iterations. A StructuredBuffer caller copies into a local array first.
+// run to count, so the capacity costs uniform space, not iterations. A caller whose sites live in a buffer copies them into a local array first.
 // The preconditions the C# functions throw for are the caller's in a shader: finite arguments, cellSize > 0, boost in [0, 4],
 // falloff > 0, smoothing in (0, 1], stretch in [1, 2], p within 2^23 cells. A zero stretchNormal means (1, 0) and needs stretch == 1.
 // cultmath_weighted_lattice_cells is math.weighted_lattice_cells: the ring pass is bounded by k <= 37 and exits as C# does, and the

From 485fe27ca493f2461801ac62b40e1de2d738c31d Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:06:15 +0200
Subject: [PATCH 13/21] cultmath map: Pass 9d (merge probe for glsl-build-dxc
 r2, phasor rename), stale open questions marked ruled; target: decided since
 the unpark

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 docs/cultmath-interval-ground-cut.md | 68 ++++++++++++++++++++++------
 docs/cultmath-tape-target.md         | 25 +++++-----
 2 files changed, 69 insertions(+), 24 deletions(-)

diff --git a/docs/cultmath-interval-ground-cut.md b/docs/cultmath-interval-ground-cut.md
index 16de3bcf..0eb8a5d2 100644
--- a/docs/cultmath-interval-ground-cut.md
+++ b/docs/cultmath-interval-ground-cut.md
@@ -9,7 +9,7 @@ the Self opened the `cultmath-tapes` campaign from pass 2; pass 3 revises the
 two CultLib cuts after their first Hands reports and the operator's challenge
 to the march, and changes the site field to envelope-then-noise; pass 4
 (section "Pass 4") revises `interval-ops` to r3 after its second Hands report
-and Soul's verdict, and names the one shipped void (Q9). Pass 5 (section "Pass 5") maps
+and Soul's verdict, and names the one shipped void (Q9, ruled `operator-shipped-void`). Pass 5 (section "Pass 5") maps
 affine forms against CultLib `main` at `a7966142`. Where a later pass and
 an earlier section disagree, the later pass wins. Where this map and the Body
 disagree, the Body wins and this map is stale.
@@ -126,9 +126,10 @@ nebula input tokens and the seed values of the ground tokens.
 **Not consumers.** Asura (its field is noise-dominated and needs no tape).
 AetheriaEve and AetheriaThing (archived). The material graph line until it returns
 after the demo (`aetheria-release:ruling:demo-material-scope`). The brush-grammar
-station, until pruning and meshing unpark. Whether Aetheria's nebula moves onto the
-span framework is not decided; until it is, the nebula consumes CultMath noise at
-its pin bump and nothing else from this line.
+station, until pruning and meshing unpark. Aetheria's nebula on the
+span framework is an option to try (ruling `aetheria-nebula-spans-as-option`), not
+yet a consumer; until a cut makes it one, the nebula consumes CultMath noise at its
+pin bump and nothing else from this line.
 
 **Invariants.**
 
@@ -750,7 +751,7 @@ and `S` from the exponent (`e = 4` gives `S ≈ 1.3 Rh`, `e = 0.25` gives
 `S ≈ 0.12 Rh`), so `(Rh, S)` are the knobs and `(Rc, e)` derived. Shipped:
 `Rh = 198`, `S = 50`, so `Rc = Rh + S = 248` and `e = −ln CARVE / ln(1 −
 (Rh/Rc)²) = 0.40`, `K = 1/30` (pass 4 corrects this line's `e ≈ 0.6, Rc ≈
-220`, which did not satisfy the formula; Q9 holds the look question).
+220`, which did not satisfy the formula; Q9 asked the look question and is ruled `operator-shipped-void`).
 
 Imagination's model (scratchpad `cavity_model.py`; the test confirms or
 refutes), 1080p, `N = 8`, per pixel for a converged frame; "ref" is the
@@ -964,7 +965,7 @@ answers the first; the second is content and stays.
 | --- | --- | --- |
 | `frustum-ball-float-crossing` | Medium | the radius is widened by a derived float32 bound (below); seven extreme families join the enclosure test; the strictness sentence leaves the C#, the HLSL and `design.md` |
 | `aetheria-far-plane-miscited` | Low | `far = 2048`, the Main Camera's (`ARPG.unity:31777`, `:31830`); the Tint camera's 1000 was the wrong camera |
-| `shipped-void-two-scenes` | Medium | one shipped void, `(Rh, S) = (198, 50)`, `(Rc, e) = (248, 0.40)` derived; the map, the site-ground spec and the test agree; the look question is Q9 |
+| `shipped-void-two-scenes` | Medium | one shipped void, `(Rh, S) = (198, 50)`, `(Rc, e) = (248, 0.40)` derived; the map, the site-ground spec and the test agree; the look question was Q9, ruled `operator-shipped-void` |
 | `lod-weights-never-exercised` | Low | configuration "LOD far" (`Rh = 4000`, `S = 50`, low camera, `f = 467`) reaches weights in `(0, 1)` and at 0; the `[w(z1), 1]` bound is recorded as a deviation with its soundness argument |
 | `stryker-timeout-survivor` | Low | 2525 named equivalent; ball radii to `1e3` so `L/r` dies to an enclosure test; every timeout hand-run; the report claims only demonstrated kills |
 
@@ -1011,7 +1012,7 @@ analytic body the second gains nothing: across a 442-wide ramp the optical
 depth exceeds 4 before the density is provably constant, so rays end inside the
 ramp and the body is never proven. The map's own rule says `(Rh, S)` are the
 knobs, so the honest choice is the first; it changes the look relative to the
-site section, hence Q9 (below). For `CARVE = 1.5` the ramp width is tied to the
+site section, hence Q9 (below; ruled (a), `operator-shipped-void`). For `CARVE = 1.5` the ramp width is tied to the
 exponent (`S/Rh = 1/√(1 − 1.5^(−1/e)) − 1`: `e = 0.4 → 0.25`, `e = 0.7 →
 0.5`, `e = 1 → 0.73`, `e = 4 → 2.2`), so "pseudo-Gaussian" and "narrow" cannot
 both be had without a third knob, and a narrow wall at `e = 4` needs
@@ -1887,9 +1888,9 @@ Aetheria twin.
 - `lattice-site-weight-source`: how a weighted lattice node gets a per-site
   weight (T7c). Re-asked as `lattice-weight-from-bodies` and ruled
   `lattice-weight-from-bodies-ruled` (node-reads-bodies).
-- `lattice-window-sound-or-measured` (open, from section
-  "lattice-weighted-cellular"): a proven ring search or a fixed measured 7x7
-  window. Gates line 4a's search loop.
+- `lattice-window-sound-or-measured` (from section "lattice-weighted-cellular"):
+  a proven ring search or a fixed measured 7x7 window. Ruled
+  `lattice-ring-exit-sound` (ring by ring until no farther cell can win).
 
 Prior art in hand: `F:\Projects\aetheria-material-path-prior-art.md` section 4
 (GPU interpreters: Fidget's crates, Dolphin ubershaders, Laine et al. on
@@ -1899,8 +1900,7 @@ found) and section 6 (IR placement); Aetheria
 filaments). Neither covers a GPU tape interpreter's register storage (dynamic
 indexing of local arrays and scratch spill, groupshared memory, Fidget-wgpu's
 `tape_interpreter.wgsl`, Keeter's MPR 2020) or per-site weight fields in
-lattice Voronoi. Both questions lack that prior art; Self runs Eyes before
-putting them.
+lattice Voronoi. Both questions have since been ruled.
 
 ### Cut sequence (Pass 7; one line each, mapped when about to run)
 
@@ -2369,6 +2369,36 @@ and 16:50 UTC (18:30 to 18:50 CEST). Logs are in the Imagination scratchpad
     form: HLSL entry built with `-Gis`, and a harness pass that adds `NoContraction` to every float op of
     both modules (about 12 lines of `spirv-dis` and `spirv-as`; `tools/device/nc.py` in the probe). That is
     127 of 127. The shipped GLSL and the C# bounds judge are unchanged. See question `glsl-gate-strict-form`.
+- **The build at main, with the rename and the strict form (Pass 9d).** Imagination `imagination-ag5-glsl`,
+  2026-10-17, scratch worktree `C:\cl-wt\imag-ag5-probe` (not pushed): `23ac4e89` merged with origin/main
+  `86cd84a3` as `69987d91` (no conflict; README.md and tools/device/gen.py auto-merged), probe commits
+  `575badb6` to `d14bfbbe` (`probe/p1.sh`, `p2.sh`, `spec.py`). Yggdrasil, `mcr.microsoft.com/dotnet/sdk:10.0` and
+  `ubuntu:24.04`; logs in the session scratchpad `imagination-ag5-glsl/p2.log` to `p4.log`.
+  - **Site arrays break the wrappers.** `wrappers.py` passes `sites[CULTMATH_MAX_SITES]` as the argument (its
+    last-token rule), and dxc refuses the three wrappers of `cultmath_power_border`,
+    `cultmath_lattice_cell_distance` and `cultmath_weighted_lattice_cells` ('no known conversion from float4 to
+    float4 [128]'). Stripping the `[..]` suffix from the argument fixes it; then the build is green: core 139
+    functions over 91 names (1554 lines, 54775 bytes), cycles 51/51 (867, 21250), phacelle 1/1 (82, 3199); zero
+    suffixed ids and zero inout.
+  - **The renamed fields survive SPIRV-Cross.** With `float4 cosine; float4 sine;` in the HLSL (HLSL only, in
+    the job), the built phacelle.glsl declares `vec4 cosine; vec4 sine;`.
+  - **The strict-form gate holds at main.** With `-Gis` on the HLSL entry and NoContraction on both modules
+    (the text `nc.py` of Pass 9c, probe only): lavapipe-glsl equals lavapipe-hlsl on 129 of 129 work items.
+    The work list is 125 fixture families (123 at `774bebb0`; the lattice loop added two) plus one
+    reference item for each of the 4 sampled affine families, so h1's 127 was 123 + 4.
+  - **The built GLSL loses the capacity override.** dxc preprocesses `CULTMATH_MAX_SITES`, so built core.glsl
+    has no mention of it and four literal `[128]` arrays. A consumer with `#define CULTMATH_MAX_SITES 4`
+    passing `vec4 s[4]` fails glslang ('no matching overloaded function'); the same consumer compiles
+    against the committed (lowered) GLSL and through dxc against the HLSL.
+  - **dxc has no spec-constant array size.** `[[vk::constant_id(7)]] const int CAP = 128;` as an array
+    parameter's length is refused ('variable length arrays are not supported in HLSL').
+  - **A SPIR-V spec constant carries it.** In the built SPIR-V exactly one constant is an array length
+    equal to 128 (id 1297), used by nothing but OpTypeArray. Made an OpSpecConstant with SpecId 0, it passes
+    spirv-val, and SPIRV-Cross ES emits `#ifndef SPIRV_CROSS_CONSTANT_ID_0` / `#define ... 128u` /
+    `const uint _1297 = SPIRV_CROSS_CONSTANT_ID_0;` with `vec4 sites[_1297]` in every site-array
+    signature. The probe's consumer defined the macro as a plain int and was refused for the uint
+    initializer, so the `uint(CULTMATH_MAX_SITES)` mapping that `cut-glsl-build-dxc.r2` writes is
+    the route, but has not been compiled yet.
 - **Capability strip.** `spirv-opt --trim-capabilities` (spirv-tools 2025.1~rc1) leaves all 14
   capabilities and both extensions in place, and SPIRV-Cross still refuses ("RayQuery requires Vulkan
   GLSL 460"). Stripping every capability except Shader and Linkage and every OpExtension in the
@@ -2436,11 +2466,23 @@ and 16:50 UTC (18:30 to 18:50 CEST). Logs are in the Imagination scratchpad
     lavapipe-hlsl result bit for bit in every family (117 of 117 measured), and the C# judge's
     bounds are re-recorded only where a family moved and equals its HLSL result.
 
+- **CultPhasor's JSON keys (model page row).** Named by `CultMathJson`; written as `cosine`/`sine` from
+  `phasor-field-rename` on, and read as either those or the legacy `cos`/`sin`, forever unless a later
+  Breaking change removes the legacy names. Decided by ruling `phasor-fields-renamed-at-source`. The
+  MessagePack wire is positional and never named the fields, so `.cc` documents are untouched both ways.
+  A reader from before the rename skips the new keys and decodes zeros (its unknown-property rule), which
+  is why the change is Breaking in both changelogs: upgrade readers before writers.
+- **The capacity through the build.** dxc cannot keep a macro and refuses spec-constant array sizes, so
+  the build turns the one array-length constant into a SPIR-V spec constant and `partition.py` maps
+  `CULTMATH_MAX_SITES` onto SPIRV-Cross's `SPIRV_CROSS_CONSTANT_ID_0` with source-copied header lines.
+  Rejected: building the GLSL per capacity (a consumer would run the build to change one number), and
+  rewriting `[128]` in the emitted text (the forbidden text post-pass). Pass 9d.
+
 ### Cut sequence (Pass 9; one line each, mapped when about to run)
 
 1. `shader-conforming-run`: spec admitted. The lavapipe job with the C# device judge, run against
    today's committed HLSL and GLSL, so the next cut is verified against a running check.
-2. `glsl-build-dxc` (spec admitted): the build, not yet the switch. `packages/cultmath/tools/glsl/`
+2. `glsl-build-dxc` (spec `cut-glsl-build-dxc.r2` admitted; r1's h1 left the gate red, Pass 9d): the build, not yet the switch. r2 merges main, carries site arrays and their capacity (a spec constant mapped to `CULTMATH_MAX_SITES`), the strict-form gate and the renamed phasor fields, and waits on `phasor-field-rename` (spec admitted: `cosine`/`sine` in C#, HLSL, GLSL and CultMathJson, legacy keys read; CultMath's next release is 0.5.0, a release cut of its own). `packages/cultmath/tools/glsl/`
    holds `build-glsl.sh`, which pins dxc v1.9.2607 (the sha above), SPIRV-Cross and SPIRV-Tools
    `vulkan-sdk-1.4.363.0`, plus one SPIR-V tool in Python. The build generates the export wrappers into
    its temp directory (never committed), compiles source plus wrappers with `-T lib_6_3 -spirv -Od`,
diff --git a/docs/cultmath-tape-target.md b/docs/cultmath-tape-target.md
index e752cc0e..74eae11b 100644
--- a/docs/cultmath-tape-target.md
+++ b/docs/cultmath-tape-target.md
@@ -108,15 +108,18 @@ source.
 - Asura does not need this campaign. Its field is noise-dominated, and its
   `A_max` shell and band-limiting already give the cheap culling.
 
-## Open before unparking
+## Decided since the unpark, and what stays open
 
-- Run the (a) spike first, or go straight to (c)?
-- Pick the interval representation (plain intervals or affine arithmetic) and
-  the noise bound strategy.
-  Affine forms for noise and warp were unparked on 2026-10-03 (ruling
-  `cultmath-tapes:ruling:affine-forms-unparked`): one shared symbol, mapped in
-  `docs/cultmath-interval-ground-cut.md`, "Pass 5".
-- Choose the bytecode register model for the HLSL interpreter, given GPU
-  register pressure.
-- Decide whether the brush-grammar station project lives in Aetheria or in
-  its own repo.
+- The spike-or-(c) choice was settled by the operator's unpark: the tape
+  unparked for Aetheria's trophic species graphs (ruling
+  `cultmath-tapes:ruling:tape-unparked-for-trophic-graphs`).
+- Interval representation: affine forms for noise and warp, unparked on
+  2026-10-03 (ruling `cultmath-tapes:ruling:affine-forms-unparked`): one
+  shared symbol, mapped in `docs/cultmath-interval-ground-cut.md`, "Pass 5".
+- Register model: the HLSL interpreter keeps its registers in groupshared
+  memory, a slice per thread, linear-scan allocated at lowering (ruling
+  `cultmath-tapes:ruling:tape-register-model-ruled`; research in
+  `docs/research/tape-register-model.md`).
+- Open: whether the brush-grammar station project lives in Aetheria or in
+  its own repo (follow-up `cultmath-tapes:follow_up:brush-grammar-station-repo`,
+  raised as an operator question when a station cut reaches the frontier).

From 28e35dc4481728ca355e6064652480412cb42963 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:25:20 +0200
Subject: [PATCH 14/21] CultMath tests: legacy CultPhasor JSON fixture written
 by the 86cd84a3 encoder

Two encodings with keys cos/sin, produced by CultMathJson at base (Yggdrasil scratch run, sha256 2903179720e2a2c974a3c64efea4ee95dec823943dd67f50df01adf650823e1a).

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 .../GameCult.Caching.Tests/Fixtures/cultphasor-json-legacy.json  | 1 +
 1 file changed, 1 insertion(+)
 create mode 100644 tests/GameCult.Caching.Tests/Fixtures/cultphasor-json-legacy.json

diff --git a/tests/GameCult.Caching.Tests/Fixtures/cultphasor-json-legacy.json b/tests/GameCult.Caching.Tests/Fixtures/cultphasor-json-legacy.json
new file mode 100644
index 00000000..c04540ff
--- /dev/null
+++ b/tests/GameCult.Caching.Tests/Fixtures/cultphasor-json-legacy.json
@@ -0,0 +1 @@
+[{"cos":{"x":1,"y":2,"z":3,"w":4},"sin":{"x":5,"y":6,"z":7,"w":8}},{"cos":{"x":-5.849812,"y":0.051139403,"z":0.14261721,"w":-0.087419346},"sin":{"x":-2.0218675,"y":0.7666904,"z":-0.22879826,"w":0.9240916}}]

From d605c70bbafe1741a4be60cd56f5279cc7b12d8e Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:25:39 +0200
Subject: [PATCH 15/21] CultPhasor.cos/.sin become .cosine/.sine in C# and HLSL
 (GLSL regenerated next)

SPIRV-Cross renames members matching GLSL builtins, so the source names change. Resolver and JSON writer accessors follow the members; the wire (positional MessagePack, JSON keys) is untouched in this commit. The committed GLSL is stale until its regeneration commit, so CommittedGlslEqualsLowering fails here.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 .../cultmath/shaders/CultMath.Phacelle.hlsl   | 12 ++++----
 packages/cultmath/src/CultMath/CultPhasor.cs  | 10 +++----
 .../tests/CultMath.Tests/PhacelleTests.cs     | 30 +++++++++----------
 .../Shaders/CultMath.Phacelle.hlsl            | 12 ++++----
 .../CultMathJson.cs                           |  4 +--
 .../CultMathResolver.cs                       |  6 ++--
 6 files changed, 37 insertions(+), 37 deletions(-)

diff --git a/packages/cultmath/shaders/CultMath.Phacelle.hlsl b/packages/cultmath/shaders/CultMath.Phacelle.hlsl
index c95aafc6..deb47813 100644
--- a/packages/cultmath/shaders/CultMath.Phacelle.hlsl
+++ b/packages/cultmath/shaders/CultMath.Phacelle.hlsl
@@ -14,8 +14,8 @@
 // against CultMath.CultPhasor, same field order.
 struct CultPhasor
 {
-    float4 cos;
-    float4 sin;
+    float4 cosine;
+    float4 sine;
 };
 
 // Johansen's Phacelle noise on 3D cells. See math.phacelle's comment (math.Phacelle.cs) for the stripe wave
@@ -84,13 +84,13 @@ CultPhasor cultmath_phacelle(float3 p, float3 side, float offset, float normaliz
         float outCos = rawCos / rawLength;
         float outSin = rawSin / rawLength;
         float3 gradLength = (rawCos * gradRawCos + rawSin * gradRawSin) / rawLength;
-        result.cos = float4((gradRawCos - outCos * gradLength) / rawLength, outCos);
-        result.sin = float4((gradRawSin - outSin * gradLength) / rawLength, outSin);
+        result.cosine = float4((gradRawCos - outCos * gradLength) / rawLength, outCos);
+        result.sine = float4((gradRawSin - outSin * gradLength) / rawLength, outSin);
     }
     else
     {
-        result.cos = float4(gradRawCos / floorLength, rawCos / floorLength);
-        result.sin = float4(gradRawSin / floorLength, rawSin / floorLength);
+        result.cosine = float4(gradRawCos / floorLength, rawCos / floorLength);
+        result.sine = float4(gradRawSin / floorLength, rawSin / floorLength);
     }
 
     return result;
diff --git a/packages/cultmath/src/CultMath/CultPhasor.cs b/packages/cultmath/src/CultMath/CultPhasor.cs
index fbc1f9d7..4b5b6a96 100644
--- a/packages/cultmath/src/CultMath/CultPhasor.cs
+++ b/packages/cultmath/src/CultMath/CultPhasor.cs
@@ -14,14 +14,14 @@ namespace CultMath;
 public struct CultPhasor
 {
     /// <summary>(&#8711;cos, cos): the normalized cosine wave and its gradient.</summary>
-    public float4 cos;
+    public float4 cosine;
 
     /// <summary>(&#8711;sin, sin): the normalized sine wave and its gradient.</summary>
-    public float4 sin;
+    public float4 sine;
 
-    public CultPhasor(float4 cos, float4 sin)
+    public CultPhasor(float4 cosine, float4 sine)
     {
-        this.cos = cos;
-        this.sin = sin;
+        this.cosine = cosine;
+        this.sine = sine;
     }
 }
diff --git a/packages/cultmath/tests/CultMath.Tests/PhacelleTests.cs b/packages/cultmath/tests/CultMath.Tests/PhacelleTests.cs
index b64f70b1..71f5b452 100644
--- a/packages/cultmath/tests/CultMath.Tests/PhacelleTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/PhacelleTests.cs
@@ -93,12 +93,12 @@ public sealed class PhacelleTests
             var actual = math.phacelle(p, side, offset, normalization);
             var expected = Evaluate(p, side, offset, normalization);
 
-            maxError = Math.Max(maxError, Math.Max(Math.Abs(actual.cos.w - expected.Cos), Math.Abs(actual.sin.w - expected.Sin)));
+            maxError = Math.Max(maxError, Math.Max(Math.Abs(actual.cosine.w - expected.Cos), Math.Abs(actual.sine.w - expected.Sin)));
             if (expected.RawLength >= 1.0 - normalization + ThresholdBand)
             {
                 // The output magnitude is 1 wherever the raw magnitude reaches 1 - normalization.
                 above++;
-                var magnitude = Math.Sqrt((double)actual.cos.w * actual.cos.w + (double)actual.sin.w * actual.sin.w);
+                var magnitude = Math.Sqrt((double)actual.cosine.w * actual.cosine.w + (double)actual.sine.w * actual.sine.w);
                 Assert.True(Math.Abs(magnitude - 1.0) < ValueTolerance, $"magnitude {magnitude} above the threshold at {p}");
             }
             else if (expected.RawLength <= 1.0 - normalization - ThresholdBand)
@@ -130,10 +130,10 @@ public sealed class PhacelleTests
             var quarter = math.phacelle(p, side, offset + 0.25f, 0.5f);
             var whole = math.phacelle(p, side, offset + 1.0f, 0.5f);
 
-            Assert.True(MathF.Abs(quarter.cos.w + basePhasor.sin.w) < 2.0e-5f);
-            Assert.True(MathF.Abs(quarter.sin.w - basePhasor.cos.w) < 2.0e-5f);
-            Assert.True(MathF.Abs(whole.cos.w - basePhasor.cos.w) < 2.0e-5f);
-            Assert.True(MathF.Abs(whole.sin.w - basePhasor.sin.w) < 2.0e-5f);
+            Assert.True(MathF.Abs(quarter.cosine.w + basePhasor.sine.w) < 2.0e-5f);
+            Assert.True(MathF.Abs(quarter.sine.w - basePhasor.cosine.w) < 2.0e-5f);
+            Assert.True(MathF.Abs(whole.cosine.w - basePhasor.cosine.w) < 2.0e-5f);
+            Assert.True(MathF.Abs(whole.sine.w - basePhasor.sine.w) < 2.0e-5f);
         }
     }
 
@@ -166,9 +166,9 @@ public sealed class PhacelleTests
             if (distance > 0.0) above++; else below++;
 
             var analytic = math.phacelle(p, side, offset, normalization);
-            var numericCos = CentralDifference(q => math.phacelle(q, side, offset, normalization).cos.w, p, GradientEps);
-            var numericSin = CentralDifference(q => math.phacelle(q, side, offset, normalization).sin.w, p, GradientEps);
-            maxError = MathF.Max(maxError, MathF.Max(MaxComponentError(numericCos, analytic.cos), MaxComponentError(numericSin, analytic.sin)));
+            var numericCos = CentralDifference(q => math.phacelle(q, side, offset, normalization).cosine.w, p, GradientEps);
+            var numericSin = CentralDifference(q => math.phacelle(q, side, offset, normalization).sine.w, p, GradientEps);
+            maxError = MathF.Max(maxError, MathF.Max(MaxComponentError(numericCos, analytic.cosine), MaxComponentError(numericSin, analytic.sine)));
         }
 
         Assert.True(above >= 150 && below >= 150, $"{above} points above and {below} below the threshold");
@@ -199,7 +199,7 @@ public sealed class PhacelleTests
             var flow = math.normalize(tangent);
             var sideDirection = math.cross(hat, flow);
             var phasor = math.phacelle(hat * radiusInCells, sideDirection * math.TAU, 0.25f, 0.5f);
-            var gradient = new float3(phasor.cos.x, phasor.cos.y, phasor.cos.z);
+            var gradient = new float3(phasor.cosine.x, phasor.cosine.y, phasor.cosine.z);
             alongFlow += Math.Abs(math.dot(gradient, flow));
             acrossFlow += Math.Abs(math.dot(gradient, sideDirection));
             used++;
@@ -232,7 +232,7 @@ public sealed class PhacelleTests
             {
                 var low = math.phacelle(SetAxis(p, axis, GetAxis(p, axis) - steps[k] * 0.5f), side, offset, 0.5f);
                 var high = math.phacelle(SetAxis(p, axis, GetAxis(p, axis) + steps[k] * 0.5f), side, offset, 0.5f);
-                maxDifference[k] = MathF.Max(maxDifference[k], MathF.Max(MathF.Abs(low.cos.w - high.cos.w), MathF.Abs(low.sin.w - high.sin.w)));
+                maxDifference[k] = MathF.Max(maxDifference[k], MathF.Max(MathF.Abs(low.cosine.w - high.cosine.w), MathF.Abs(low.sine.w - high.sine.w)));
             }
         }
 
@@ -260,8 +260,8 @@ public sealed class PhacelleTests
             var pruned = math.phacelle(p, side, offset, normalization);
             var unpruned = math.phacelle(p, side, offset, normalization, false);
 
-            AssertBitEqual(unpruned.cos, pruned.cos);
-            AssertBitEqual(unpruned.sin, pruned.sin);
+            AssertBitEqual(unpruned.cosine, pruned.cosine);
+            AssertBitEqual(unpruned.sine, pruned.sine);
         }
     }
 
@@ -325,8 +325,8 @@ public sealed class PhacelleTests
             var pruned = math.phacelle(p, PruneCutSide, PruneCutOffset, PruneCutNormalization);
             var unpruned = math.phacelle(p, PruneCutSide, PruneCutOffset, PruneCutNormalization, false);
 
-            AssertBitEqual(unpruned.cos, pruned.cos);
-            AssertBitEqual(unpruned.sin, pruned.sin);
+            AssertBitEqual(unpruned.cosine, pruned.cosine);
+            AssertBitEqual(unpruned.sine, pruned.sine);
         }
     }
 
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.Phacelle.hlsl b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.Phacelle.hlsl
index c95aafc6..deb47813 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.Phacelle.hlsl
+++ b/packages/cultmath/unity/org.gamecult.cultmath/Shaders/CultMath.Phacelle.hlsl
@@ -14,8 +14,8 @@
 // against CultMath.CultPhasor, same field order.
 struct CultPhasor
 {
-    float4 cos;
-    float4 sin;
+    float4 cosine;
+    float4 sine;
 };
 
 // Johansen's Phacelle noise on 3D cells. See math.phacelle's comment (math.Phacelle.cs) for the stripe wave
@@ -84,13 +84,13 @@ CultPhasor cultmath_phacelle(float3 p, float3 side, float offset, float normaliz
         float outCos = rawCos / rawLength;
         float outSin = rawSin / rawLength;
         float3 gradLength = (rawCos * gradRawCos + rawSin * gradRawSin) / rawLength;
-        result.cos = float4((gradRawCos - outCos * gradLength) / rawLength, outCos);
-        result.sin = float4((gradRawSin - outSin * gradLength) / rawLength, outSin);
+        result.cosine = float4((gradRawCos - outCos * gradLength) / rawLength, outCos);
+        result.sine = float4((gradRawSin - outSin * gradLength) / rawLength, outSin);
     }
     else
     {
-        result.cos = float4(gradRawCos / floorLength, rawCos / floorLength);
-        result.sin = float4(gradRawSin / floorLength, rawSin / floorLength);
+        result.cosine = float4(gradRawCos / floorLength, rawCos / floorLength);
+        result.sine = float4(gradRawSin / floorLength, rawSin / floorLength);
     }
 
     return result;
diff --git a/src/GameCult.Caching.MessagePack/CultMathJson.cs b/src/GameCult.Caching.MessagePack/CultMathJson.cs
index ba83410d..12958f03 100644
--- a/src/GameCult.Caching.MessagePack/CultMathJson.cs
+++ b/src/GameCult.Caching.MessagePack/CultMathJson.cs
@@ -511,8 +511,8 @@ public static class CultMathJson
                 a => new CultPhasor(new float4(a[0], a[1], a[2], a[3]), new float4(a[4], a[5], a[6], a[7])),
                 (v, a) =>
                 {
-                    a[0] = v.cos.x; a[1] = v.cos.y; a[2] = v.cos.z; a[3] = v.cos.w;
-                    a[4] = v.sin.x; a[5] = v.sin.y; a[6] = v.sin.z; a[7] = v.sin.w;
+                    a[0] = v.cosine.x; a[1] = v.cosine.y; a[2] = v.cosine.z; a[3] = v.cosine.w;
+                    a[4] = v.sine.x; a[5] = v.sine.y; a[6] = v.sine.z; a[7] = v.sine.w;
                 }),
             Add<SpanNoise, float>(f, new Fields<float>(("field", Xyzw<float>()), ("curvature", Val<float>()), ("fold", Val<float>())),
                 a => new SpanNoise(new float4(a[0], a[1], a[2], a[3]), a[4], a[5]),
diff --git a/src/GameCult.Caching.MessagePack/CultMathResolver.cs b/src/GameCult.Caching.MessagePack/CultMathResolver.cs
index 95937282..02ee980c 100644
--- a/src/GameCult.Caching.MessagePack/CultMathResolver.cs
+++ b/src/GameCult.Caching.MessagePack/CultMathResolver.cs
@@ -221,7 +221,7 @@ public sealed class CultMathResolver : IFormatterResolver
                     }
                     return value;
                 }),
-            Shape<CultPhasor>((ref MessagePackWriter w, CultPhasor v) => { w.WriteArrayHeader(2); PutFloat4(ref w, v.cos); PutFloat4(ref w, v.sin); },
+            Shape<CultPhasor>((ref MessagePackWriter w, CultPhasor v) => { w.WriteArrayHeader(2); PutFloat4(ref w, v.cosine); PutFloat4(ref w, v.sine); },
                 (ref MessagePackReader r) =>
                 {
                     var value = default(CultPhasor);
@@ -229,8 +229,8 @@ public sealed class CultMathResolver : IFormatterResolver
                     {
                         switch (i)
                         {
-                            case 0: value.cos = GetFloat4(ref r); break;
-                            case 1: value.sin = GetFloat4(ref r); break;
+                            case 0: value.cosine = GetFloat4(ref r); break;
+                            case 1: value.sine = GetFloat4(ref r); break;
                             default: r.Skip(); break;
                         }
                     }

From c027d3f88464594ebe862c3ca2bc2793406cb50f Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:28:00 +0200
Subject: [PATCH 16/21] CultMath.Phacelle.glsl regenerated for cosine/sine

Written by CULTMATH_WRITE_GLSL=1 on Yggdrasil (sdk:10.0) at d605c70b; sha256 21eef3c38cc609909444c906a1ef965f01b541f2301023a722e64ecc4c846387. glsl-parity.json and device-bounds-lavapipe.txt are untouched by the regeneration.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 packages/cultmath/shaders/CultMath.Phacelle.glsl | 12 ++++++------
 1 file changed, 6 insertions(+), 6 deletions(-)

diff --git a/packages/cultmath/shaders/CultMath.Phacelle.glsl b/packages/cultmath/shaders/CultMath.Phacelle.glsl
index 11405fa2..c22c67c4 100644
--- a/packages/cultmath/shaders/CultMath.Phacelle.glsl
+++ b/packages/cultmath/shaders/CultMath.Phacelle.glsl
@@ -14,8 +14,8 @@
 // against CultMath.CultPhasor, same field order.
 struct CultPhasor
 {
-    vec4 cos;
-    vec4 sin;
+    vec4 cosine;
+    vec4 sine;
 };
 
 // Johansen's Phacelle noise on 3D cells. See math.phacelle's comment (math.Phacelle.cs) for the stripe wave
@@ -84,13 +84,13 @@ CultPhasor cultmath_phacelle(vec3 p, vec3 side, float offset, float normalizatio
         float outCos = rawCos / rawLength;
         float outSin = rawSin / rawLength;
         vec3 gradLength = (rawCos * gradRawCos + rawSin * gradRawSin) / rawLength;
-        result.cos = vec4((gradRawCos - outCos * gradLength) / rawLength, outCos);
-        result.sin = vec4((gradRawSin - outSin * gradLength) / rawLength, outSin);
+        result.cosine = vec4((gradRawCos - outCos * gradLength) / rawLength, outCos);
+        result.sine = vec4((gradRawSin - outSin * gradLength) / rawLength, outSin);
     }
     else
     {
-        result.cos = vec4(gradRawCos / floorLength, rawCos / floorLength);
-        result.sin = vec4(gradRawSin / floorLength, rawSin / floorLength);
+        result.cosine = vec4(gradRawCos / floorLength, rawCos / floorLength);
+        result.sine = vec4(gradRawSin / floorLength, rawSin / floorLength);
     }
 
     return result;

From 58baccce787d1a40c75eb81757b89b83d157bb8a Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:28:09 +0200
Subject: [PATCH 17/21] CultMathJson writes CultPhasor as cosine/sine and still
 reads cos/sin

Fields takes an optional legacy name per field, matched on read only and mapped to the same index as the current name, so a legacy and a current name in one object are the same property and the duplicate rules decide (refused when AllowDuplicateProperties is false, last wins otherwise). Writing never emits a legacy name. MessagePack bytes are unchanged.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 .../CultMathJson.cs                           | 23 +++++++--
 .../CultMathResolver.cs                       |  2 +-
 .../CultMathJsonTests.cs                      | 51 ++++++++++++++++++-
 3 files changed, 69 insertions(+), 7 deletions(-)

diff --git a/src/GameCult.Caching.MessagePack/CultMathJson.cs b/src/GameCult.Caching.MessagePack/CultMathJson.cs
index 12958f03..65dea503 100644
--- a/src/GameCult.Caching.MessagePack/CultMathJson.cs
+++ b/src/GameCult.Caching.MessagePack/CultMathJson.cs
@@ -14,7 +14,7 @@ namespace GameCult.Caching.MessagePack;
 /// The canonical System.Text.Json shape of every public CultMath value type, the JSON twin of
 /// <see cref="CultMathResolver"/>. Vectors, quaternions and colors are objects keyed by their
 /// field names (<c>{"x":1,"y":2}</c>), matrices are arrays of row objects, <c>rect</c> is
-/// <c>{"min":..,"max":..}</c>, <c>CultCellular</c> is <c>{"nearest":..,"edge":..,"id":..}</c>, <c>CultPhasor</c> is <c>{"cos":..,"sin":..}</c>, <c>SpanNoise</c> is <c>{"field":..,"curvature":..,"fold":..}</c>, <c>SpanPath</c> is <c>{"midpoint":..,"velocity":..,"speed":..,"acceleration":..,"halfLength":..}</c>, <c>SpanStage</c> is <c>{"frequency":..,"stretch":..,"axis":..,"shift":..,"offset":..,"octaveStep":..}</c>, and <c>CultSiteCells</c> is <c>{"nearest":..,"second":..,"nearestSite":..,"secondSite":..}</c>.
+/// <c>{"min":..,"max":..}</c>, <c>CultCellular</c> is <c>{"nearest":..,"edge":..,"id":..}</c>, <c>CultPhasor</c> is <c>{"cosine":..,"sine":..}</c> (reading also accepts the legacy <c>cos</c>/<c>sin</c> names), <c>SpanNoise</c> is <c>{"field":..,"curvature":..,"fold":..}</c>, <c>SpanPath</c> is <c>{"midpoint":..,"velocity":..,"speed":..,"acceleration":..,"halfLength":..}</c>, <c>SpanStage</c> is <c>{"frequency":..,"stretch":..,"axis":..,"shift":..,"offset":..,"octaveStep":..}</c>, and <c>CultSiteCells</c> is <c>{"nearest":..,"second":..,"nearestSite":..,"secondSite":..}</c>.
 /// Property names are fixed: <c>PropertyNamingPolicy</c> does not rename them, and
 /// <c>PropertyNameCaseInsensitive</c> makes reading case-insensitive.
 /// <para>
@@ -270,14 +270,24 @@ public static class CultMathJson
     {
         private readonly string[] names;
         private readonly byte[][] utf8Names;
+        private readonly string?[] legacyNames;
+        private readonly byte[]?[] legacyUtf8Names;
         private readonly JsonEncodedText[] encoded;
         private readonly Node<S>[] children;
         private readonly int[] offsets;
 
         public Fields(params (string Name, Node<S> Child)[] fields)
+            : this(Array.ConvertAll(fields, f => (f.Name, f.Child, (string?)null)))
+        {
+        }
+
+        // A legacy name is matched on read only and maps to the same field as its current name.
+        public Fields(params (string Name, Node<S> Child, string? Legacy)[] fields)
         {
             names = new string[fields.Length];
             utf8Names = new byte[fields.Length][];
+            legacyNames = new string?[fields.Length];
+            legacyUtf8Names = new byte[]?[fields.Length];
             encoded = new JsonEncodedText[fields.Length];
             children = new Node<S>[fields.Length];
             offsets = new int[fields.Length];
@@ -285,6 +295,8 @@ public static class CultMathJson
             {
                 names[i] = fields[i].Name;
                 utf8Names[i] = Encoding.UTF8.GetBytes(fields[i].Name);
+                legacyNames[i] = fields[i].Legacy;
+                legacyUtf8Names[i] = fields[i].Legacy is { } legacy ? Encoding.UTF8.GetBytes(legacy) : null;
                 encoded[i] = JsonEncodedText.Encode(fields[i].Name);
                 children[i] = fields[i].Child;
                 offsets[i] = Count;
@@ -339,13 +351,14 @@ public static class CultMathJson
             if (!ignoreCase)
             {
                 for (var i = 0; i < utf8Names.Length; i++)
-                    if (r.ValueTextEquals(utf8Names[i])) return i;
+                    if (r.ValueTextEquals(utf8Names[i]) || (legacyUtf8Names[i] is { } legacy && r.ValueTextEquals(legacy))) return i;
                 return -1;
             }
 
             var name = r.GetString()!;
             for (var i = 0; i < names.Length; i++)
-                if (string.Equals(names[i], name, StringComparison.OrdinalIgnoreCase)) return i;
+                if (string.Equals(names[i], name, StringComparison.OrdinalIgnoreCase)
+                    || (legacyNames[i] is { } legacy && string.Equals(legacy, name, StringComparison.OrdinalIgnoreCase))) return i;
             return -1;
         }
     }
@@ -481,7 +494,7 @@ public static class CultMathJson
             Add<Random, uint>(UIntScalar.Instance, new Fields<uint>(("state", Val<uint>())),
                 a => new Random { state = a[0] }, (v, a) => a[0] = v.state),
 
-            // Compositions: matrices are arrays of row objects, rect is {min, max}, CultCellular is {nearest, edge, id}, CultPhasor is {cos, sin}, SpanNoise is {field, curvature, fold}, SpanPath is {midpoint, velocity, speed, acceleration, halfLength}, SpanStage is {frequency, stretch, axis, shift, offset, octaveStep}, CultSiteCells is {nearest, second, nearestSite, secondSite}.
+            // Compositions: matrices are arrays of row objects, rect is {min, max}, CultCellular is {nearest, edge, id}, CultPhasor is {cosine, sine}, SpanNoise is {field, curvature, fold}, SpanPath is {midpoint, velocity, speed, acceleration, halfLength}, SpanStage is {frequency, stretch, axis, shift, offset, octaveStep}, CultSiteCells is {nearest, second, nearestSite, secondSite}.
             Add<float2x2, float>(f, new Rows<float>(2, Xy<float>()),
                 a => new float2x2(a[0], a[1], a[2], a[3]),
                 (v, a) => { a[0] = v[0].x; a[1] = v[0].y; a[2] = v[1].x; a[3] = v[1].y; }),
@@ -507,7 +520,7 @@ public static class CultMathJson
                     a[4] = v.edge.x; a[5] = v.edge.y; a[6] = v.edge.z; a[7] = v.edge.w;
                     a[8] = v.id;
                 }),
-            Add<CultPhasor, float>(f, new Fields<float>(("cos", Xyzw<float>()), ("sin", Xyzw<float>())),
+            Add<CultPhasor, float>(f, new Fields<float>(("cosine", Xyzw<float>(), "cos"), ("sine", Xyzw<float>(), "sin")),
                 a => new CultPhasor(new float4(a[0], a[1], a[2], a[3]), new float4(a[4], a[5], a[6], a[7])),
                 (v, a) =>
                 {
diff --git a/src/GameCult.Caching.MessagePack/CultMathResolver.cs b/src/GameCult.Caching.MessagePack/CultMathResolver.cs
index 02ee980c..048b7f87 100644
--- a/src/GameCult.Caching.MessagePack/CultMathResolver.cs
+++ b/src/GameCult.Caching.MessagePack/CultMathResolver.cs
@@ -180,7 +180,7 @@ public sealed class CultMathResolver : IFormatterResolver
                     return value;
                 }),
 
-            // Compositions: matrices are rows, rect is [min, max], CultCellular is [nearest, edge, id], CultPhasor is [cos, sin], SpanNoise is [field, curvature, fold], SpanPath is [midpoint, velocity, speed, acceleration, halfLength], SpanStage is [frequency, stretch, axis, shift, offset, octaveStep], CultSiteCells is [nearest, second, nearestSite, secondSite].
+            // Compositions: matrices are rows, rect is [min, max], CultCellular is [nearest, edge, id], CultPhasor is [cosine, sine], SpanNoise is [field, curvature, fold], SpanPath is [midpoint, velocity, speed, acceleration, halfLength], SpanStage is [frequency, stretch, axis, shift, offset, octaveStep], CultSiteCells is [nearest, second, nearestSite, secondSite].
             Shape<float2x2>((ref MessagePackWriter w, float2x2 v) => { w.WriteArrayHeader(2); PutFloat2(ref w, v[0]); PutFloat2(ref w, v[1]); },
                 (ref MessagePackReader r) =>
                 {
diff --git a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
index 4ebd552b..ef8ea3d6 100644
--- a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
+++ b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
@@ -44,7 +44,7 @@ namespace GameCult.Caching.Tests
             Json(new CultCellular(new float4(1f, 2f, 3f, 4f), new float4(5f, 6f, 7f, 8f), 0.25f)).Should().Be(
                 """{"nearest":{"x":1,"y":2,"z":3,"w":4},"edge":{"x":5,"y":6,"z":7,"w":8},"id":0.25}""");
             Json(new CultPhasor(new float4(1f, 2f, 3f, 4f), new float4(5f, 6f, 7f, 8f))).Should().Be(
-                """{"cos":{"x":1,"y":2,"z":3,"w":4},"sin":{"x":5,"y":6,"z":7,"w":8}}""");
+                """{"cosine":{"x":1,"y":2,"z":3,"w":4},"sine":{"x":5,"y":6,"z":7,"w":8}}""");
             Json(new SpanNoise(new float4(1f, 2f, 3f, 4f), 0.25f, 0.5f)).Should().Be(
                 """{"field":{"x":1,"y":2,"z":3,"w":4},"curvature":0.25,"fold":0.5}""");
             Json(new SpanPath { midpoint = new float3(1f, 2f, 3f), velocity = new float3(4f, 5f, 6f), speed = 7f, acceleration = 8f, halfLength = 9f }).Should().Be(
@@ -92,6 +92,55 @@ namespace GameCult.Caching.Tests
             Parse<float2?>("null").Should().BeNull();
         }
 
+        [Test]
+        public void Reading_AcceptsTheLegacyPhasorNames()
+        {
+            // The fixture is what the 0.4.1-era encoder wrote: keys cos/sin.
+            var path = System.IO.Path.Combine(TestContext.CurrentContext.TestDirectory, "Fixtures", "cultphasor-json-legacy.json");
+            var legacy = Parse<CultPhasor[]>(System.IO.File.ReadAllText(path));
+            var current = new[]
+            {
+                new CultPhasor(new float4(1f, 2f, 3f, 4f), new float4(5f, 6f, 7f, 8f)),
+                math.phacelle(new float3(0.3f, 1.7f, -2.2f), new float3(6.2831853f, 0f, 0f), 0.25f, 0.5f),
+            };
+            legacy.Should().HaveCount(2);
+            for (var i = 0; i < 2; i++)
+            {
+                BitsOf(legacy[i]).Should().Equal(BitsOf(current[i]));
+                BitsOf(Parse<CultPhasor>(Json(current[i]))).Should().Equal(BitsOf(current[i]));
+            }
+
+            var caseInsensitive = new JsonSerializerOptions { PropertyNameCaseInsensitive = true }.AddCultMathConverters();
+            BitsOf(JsonSerializer.Deserialize<CultPhasor>("""{"COS":{"x":1,"y":2,"z":3,"w":4},"Sin":{"x":5,"y":6,"z":7,"w":8}}""", caseInsensitive))
+                .Should().Equal(BitsOf(current[0]));
+        }
+
+        [Test]
+        public void Reading_RefusesALegacyAndCurrentNameTogether()
+        {
+            var property = typeof(JsonSerializerOptions).GetProperty("AllowDuplicateProperties");
+            Assert.That(property, Is.Not.Null, "the test runtime's System.Text.Json has AllowDuplicateProperties");
+            var strict = new JsonSerializerOptions().AddCultMathConverters();
+            property!.SetValue(strict, false);
+            Action both = () => JsonSerializer.Deserialize<CultPhasor>("""{"cos":{"x":1},"cosine":{"x":2}}""", strict);
+            both.Should().Throw<JsonException>().WithMessage("*appears more than once*");
+            Action reversed = () => JsonSerializer.Deserialize<CultPhasor>("""{"sine":{"x":1},"sin":{"x":2}}""", strict);
+            reversed.Should().Throw<JsonException>().WithMessage("*appears more than once*");
+
+            // With duplicates allowed the later property replaces the earlier one, as for any repeated name.
+            Parse<CultPhasor>("""{"cos":{"x":1,"y":9},"cosine":{"x":2}}""").cosine.Should().Be(new float4(2f, 0f, 0f, 0f));
+        }
+
+        [Test]
+        public void Writing_NeverEmitsLegacyNames()
+        {
+            using var document = JsonDocument.Parse(Json(new CultPhasor(new float4(1f, 1f, 1f, 1f), new float4(2f, 2f, 2f, 2f))));
+            document.RootElement.EnumerateObject().Select(p => p.Name).Should().Equal("cosine", "sine");
+        }
+
+        private static int[] BitsOf(CultPhasor v) => new[] { v.cosine.x, v.cosine.y, v.cosine.z, v.cosine.w, v.sine.x, v.sine.y, v.sine.z, v.sine.w }
+            .Select(BitConverter.SingleToInt32Bits).ToArray();
+
         [Test]
         public void Reading_RefusesShapesThatAreNotTheType()
         {

From 1330362235cc47cc8286af1d3efd8192cdc8428f Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:28:25 +0200
Subject: [PATCH 18/21] CultPhasor rename: README, design note and both
 changelogs

cultmath-unity [Unreleased] and cultlib [Unreleased] carry the Breaking entries; no version bump, no tag.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 packages/cultmath/docs/design.md                         | 2 +-
 .../cultmath/unity/org.gamecult.cultmath/CHANGELOG.md    | 9 +++++++++
 src/GameCult.Caching.MessagePack/README.md               | 2 +-
 unity/org.gamecult.cultlib/CHANGELOG.md                  | 4 ++++
 4 files changed, 15 insertions(+), 2 deletions(-)

diff --git a/packages/cultmath/docs/design.md b/packages/cultmath/docs/design.md
index 62c6ed00..3b63f4d2 100644
--- a/packages/cultmath/docs/design.md
+++ b/packages/cultmath/docs/design.md
@@ -429,7 +429,7 @@ together, laid out as `float4(gradient.xyz, value.w)`, with no value-only twin
 - `phacelle(float3 p, float3 side, float offset, float normalization)` is Rune
   Skovbo Johansen's Phacelle noise ("phase + cell": a stripe pattern built by
   blending one cosine/sine wave per jittered cell), generalised to 3D cells. It
-  returns `CultPhasor { cos, sin }`, each `(∇, value)`. `side` is the stripe
+  returns `CultPhasor { cosine, sine }`, each `(∇, value)`. `side` is the stripe
   wave vector, whose length is 2π times the stripe frequency; in 3D the
   perpendicular to the flow is not unique, so the caller chooses it (on a unit
   sphere, `cross(p̂, flow)`). `offset` is the phase in cycles. It visits 4×4×4
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
index 21511bc8..d8b27dc3 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
+++ b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
@@ -5,6 +5,15 @@ All notable changes to this package are documented in this file.
 Earlier releases (0.2.0-0.2.3) predate this package's changelog and are not
 backfilled here; see `docs/semver-policy.md` for why.
 
+## [Unreleased]
+
+### Breaking
+
+- `CultPhasor.cos` and `.sin` are now `.cosine` and `.sine` in C#, HLSL and GLSL,
+  constructor parameters included, because SPIRV-Cross renames members that match
+  GLSL builtins. This is a minor bump on 0.y.z, so the next cultmath-unity release
+  is 0.5.0.
+
 ## [0.4.1]
 
 ### Fixed
diff --git a/src/GameCult.Caching.MessagePack/README.md b/src/GameCult.Caching.MessagePack/README.md
index a03a67c4..dfc7bff6 100644
--- a/src/GameCult.Caching.MessagePack/README.md
+++ b/src/GameCult.Caching.MessagePack/README.md
@@ -101,7 +101,7 @@ broken graph whole (an `ExprGraphException` naming the rule), so a consumer
 | `float2x2`, `float3x3` | array of row vectors (row-major) | array of row objects |
 | `rect` | `[min, max]` of `float2` | `{"min":{..},"max":{..}}` |
 | `CultCellular` | `[nearest, edge, id]` | `{"nearest":{..},"edge":{..},"id":..}` |
-| `CultPhasor` | `[cos, sin]` of `float4` | `{"cos":{..},"sin":{..}}` |
+| `CultPhasor` | `[cosine, sine]` of `float4` | `{"cosine":{..},"sine":{..}}` (reads legacy `cos`/`sin`) |
 | `CultSiteCells` | `[nearest, second, nearestSite, secondSite]` | `{"nearest":{..},"second":{..},"nearestSite":..,"secondSite":..}` |
 
 Floats are MessagePack float32 (`0xCA`), doubles float64 (`0xCB`), integers the
diff --git a/unity/org.gamecult.cultlib/CHANGELOG.md b/unity/org.gamecult.cultlib/CHANGELOG.md
index 9d54e996..7b0093d2 100644
--- a/unity/org.gamecult.cultlib/CHANGELOG.md
+++ b/unity/org.gamecult.cultlib/CHANGELOG.md
@@ -6,6 +6,10 @@ All notable changes to this package are documented in this file.
 
 ### Breaking
 
+- `CultMathJson` writes `CultPhasor` as `{"cosine":..,"sine":..}` and still reads
+  the old `cos`/`sin` keys. A reader from before this change skips the new keys
+  and decodes zeros, so upgrade readers before writers. MessagePack bytes are
+  unchanged.
 - CultCache refuses an unknown union arm on read and an unnamed union subtype on
   write. A payload whose arm key the union does not declare used to decode to
   `null` (and the next save wrote the loss back); a value whose type the union

From 841b11db948a31bff9171edafd020f11d68752a1 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 19:44:10 +0200
Subject: [PATCH 19/21] CultMathJson tests: unknown names are skipped under
 case-insensitive reading

Kills the surviving Stryker mutant in Fields.IndexOf's case-insensitive loop and covers its not-found return.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 tests/GameCult.Caching.Tests/CultMathJsonTests.cs | 8 ++++++++
 1 file changed, 8 insertions(+)

diff --git a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
index ef8ea3d6..54e01e24 100644
--- a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
+++ b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
@@ -131,6 +131,14 @@ namespace GameCult.Caching.Tests
             Parse<CultPhasor>("""{"cos":{"x":1,"y":9},"cosine":{"x":2}}""").cosine.Should().Be(new float4(2f, 0f, 0f, 0f));
         }
 
+        [Test]
+        public void Reading_SkipsUnknownNamesWhenCaseInsensitive()
+        {
+            var options = new JsonSerializerOptions { PropertyNameCaseInsensitive = true }.AddCultMathConverters();
+            JsonSerializer.Deserialize<CultPhasor>("""{"extra":[1,2],"COSINE":{"x":3},"coss":{"x":4}}""", options).cosine.x.Should().Be(3f);
+            JsonSerializer.Deserialize<float2>("""{"X":1,"q":2,"Y":3}""", options).Should().Be(new float2(1f, 3f));
+        }
+
         [Test]
         public void Writing_NeverEmitsLegacyNames()
         {

From 3bf9f7040a5e9f77382e529e575e29a5044ddb00 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 20:33:44 +0200
Subject: [PATCH 20/21] CultMathJson tests: legacy phasor names under Disallow,
 and a third occurrence is a duplicate

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 .../CultMathJsonTests.cs                      | 24 +++++++++++++++++++
 1 file changed, 24 insertions(+)

diff --git a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
index 54e01e24..33753074 100644
--- a/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
+++ b/tests/GameCult.Caching.Tests/CultMathJsonTests.cs
@@ -131,6 +131,30 @@ namespace GameCult.Caching.Tests
             Parse<CultPhasor>("""{"cos":{"x":1,"y":9},"cosine":{"x":2}}""").cosine.Should().Be(new float4(2f, 0f, 0f, 0f));
         }
 
+        [Test]
+        public void Reading_AcceptsTheLegacyPhasorNamesUnderDisallow()
+        {
+            var options = new JsonSerializerOptions { UnmappedMemberHandling = JsonUnmappedMemberHandling.Disallow }.AddCultMathConverters();
+            var phasor = JsonSerializer.Deserialize<CultPhasor>("""{"cos":{"x":1,"y":2,"z":3,"w":4},"sin":{"x":5,"y":6,"z":7,"w":8}}""", options);
+            BitsOf(phasor).Should().Equal(BitsOf(new CultPhasor(new float4(1f, 2f, 3f, 4f), new float4(5f, 6f, 7f, 8f))));
+            Action unknown = () => JsonSerializer.Deserialize<CultPhasor>("""{"cos":{"x":1},"coss":{"x":2}}""", options);
+            unknown.Should().Throw<JsonException>().WithMessage("*not a component*");
+        }
+
+        [Test]
+        public void Reading_TreatsAThirdOccurrenceOfAPhasorNameAsADuplicate()
+        {
+            var property = typeof(JsonSerializerOptions).GetProperty("AllowDuplicateProperties");
+            Assert.That(property, Is.Not.Null, "the test runtime's System.Text.Json has AllowDuplicateProperties");
+            var strict = new JsonSerializerOptions().AddCultMathConverters();
+            property!.SetValue(strict, false);
+            Action thrice = () => JsonSerializer.Deserialize<CultPhasor>("""{"cos":{"x":1},"cosine":{"x":2},"cos":{"x":3}}""", strict);
+            thrice.Should().Throw<JsonException>().WithMessage("*appears more than once*");
+
+            // Allowed, the last occurrence replaces the whole value, including after a third.
+            Parse<CultPhasor>("""{"cos":{"x":1,"y":9},"cosine":{"x":2},"cos":{"z":3}}""").cosine.Should().Be(new float4(0f, 0f, 3f, 0f));
+        }
+
         [Test]
         public void Reading_SkipsUnknownNamesWhenCaseInsensitive()
         {

From 4391ed23f994db8be743fc99b36a94fc361e6a93 Mon Sep 17 00:00:00 2001
From: Meta Vens <rwvens@hotmail.com>
Date: Sat, 17 Oct 2026 20:33:45 +0200
Subject: [PATCH 21/21] CHANGELOG: the old CultPhasor reader decodes zeros by
 default and throws under Disallow

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
---
 unity/org.gamecult.cultlib/CHANGELOG.md | 7 ++++---
 1 file changed, 4 insertions(+), 3 deletions(-)

diff --git a/unity/org.gamecult.cultlib/CHANGELOG.md b/unity/org.gamecult.cultlib/CHANGELOG.md
index 7b0093d2..097fcada 100644
--- a/unity/org.gamecult.cultlib/CHANGELOG.md
+++ b/unity/org.gamecult.cultlib/CHANGELOG.md
@@ -7,9 +7,10 @@ All notable changes to this package are documented in this file.
 ### Breaking
 
 - `CultMathJson` writes `CultPhasor` as `{"cosine":..,"sine":..}` and still reads
-  the old `cos`/`sin` keys. A reader from before this change skips the new keys
-  and decodes zeros, so upgrade readers before writers. MessagePack bytes are
-  unchanged.
+  the old `cos`/`sin` keys. A reader from before this change does not know the
+  new keys: with default options it skips them and decodes zeros, and with
+  `UnmappedMemberHandling.Disallow` it throws. Upgrade readers before writers.
+  MessagePack bytes are unchanged.
 - CultCache refuses an unknown union arm on read and an unnamed union subtype on
   write. A payload whose arm key the union does not declare used to decode to
   `null` (and the next save wrote the loss back); a value whose type the union