diff --git a/packages/cultmath/docs/design.md b/packages/cultmath/docs/design.md
index cf40ed12..a3c1519f 100644
--- a/packages/cultmath/docs/design.md
+++ b/packages/cultmath/docs/design.md
@@ -371,9 +371,11 @@ together, laid out as `float4(gradient.xyz, value.w)`, with no value-only twin
   pins the continuity. Ties in the offset `x0` resolve in Gustavson's
   `simplexnoise1234` order (x over y, y over z, x over z), a total order, so the
   four corners are always a simplex. Upstream's `step` compares are cyclic: where
-  the three components are equal, which includes the origin and every
-  `(t, t, t)`, the corners repeat the origin vertex and the value jumps by about
-  0.77 near the origin and up to 1.56 at magnitudes of 64 and above. `NoiseGradTests.SnoiseIsContinuousOnTheSimplexDiagonal` pins the order.
+  the three components are equal, which is every input whose differences `y - x`
+  and `z - x` are whole numbers (every integer point, the origin and every
+  `(t, t, t)` among them), the corners repeat the origin vertex and the value
+  jumps by about 0.77 near the origin and up to 1.56 at magnitudes of 64 and
+  above. `SnoiseTieScopeTests` pins the set against the 0.3.0 values. `NoiseGradTests.SnoiseIsContinuousOnTheSimplexDiagonal` pins the order.
 - `snoise_grad(float3 p)` carries `snoise(float3)` to value-and-gradient form,
   following the differentiation in webgl-noise `src/noise3Dgrad.glsl` (Ashima
   Arts / Ian McEwan, MIT), which uses the same radius, permutation and scale as
diff --git a/packages/cultmath/tests/CultMath.Tests/NoiseGradTests.cs b/packages/cultmath/tests/CultMath.Tests/NoiseGradTests.cs
index 153886db..3fe922f9 100644
--- a/packages/cultmath/tests/CultMath.Tests/NoiseGradTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/NoiseGradTests.cs
@@ -192,8 +192,9 @@ public sealed class NoiseGradTests
 
     // The simplex diagonals are where x0's three components compare equal. The tie rule must be a total
     // order there (math.snoise): with a cyclic or all-strict compare the four corners stop being a
-    // simplex and the value jumps on the line (t, t, t), lattice diagonals included: about 0.77 near the
-    // origin, up to 1.56 at magnitudes of 64 and above.
+    // simplex and the value jumps wherever x0 has three equal components (inputs whose differences y - x and
+    // z - x are whole numbers, the line (t, t, t) among them): about 0.77 near the origin, up to 1.56 at
+    // magnitudes of 64 and above. SnoiseTieScopeTests pins the set against the 0.3.0 values.
     [Fact]
     public void SnoiseIsContinuousOnTheSimplexDiagonal()
     {
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
index fcc5ca0e..734568d3 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
+++ b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
@@ -12,13 +12,22 @@ backfilled here; see `docs/semver-policy.md` for why.
 - `math.snoise(float3)` and `math.snoise_grad`, and their HLSL mirrors in
   `Shaders/CultMath.hlsl`, now resolve ties among the components of the cell
   offset in a fixed order: x over y, y over z, x over z. The cyclic rule they
-  used before made the origin and every point on the `(t, t, t)` diagonal read a
-  different function from the points beside it. Values change at the origin and
-  on the `(t, t, t)` diagonal and nowhere else; off that tie set the results are
-  bit-identical to 0.3.0. `snoise` is now continuous across the diagonal to
-  within 1e-4 over two ulps either side (`NoiseGradTests`,
-  `SnoiseIsContinuousOnTheSimplexDiagonal`). Content seeded from `snoise` at
-  those points changes; regenerate it when you take this version.
+  used before read a different function wherever the three components of the
+  cell offset are equal. That is every input whose coordinate differences
+  `y - x` and `z - x` are whole numbers: every integer point (the origin
+  included), and the whole `(1, 1, 1)` line through each of them (`(t, t, t)`
+  among them). On that set values change by up to 0.776; for example
+  `snoise(0, 0, 0)` was -0.4358730 and is 0, `snoise(5, 0, 0)` was 0.7076616 and
+  is 0.671713, and `snoise(1, 2, 3)` was 0.22423841 and is 0. Float32 rounding
+  decides whether a given input ties, and an input that ties may still keep its
+  value; measured over random integer points, about 97% change. Off that set
+  the results are bit-identical to 0.3.0
+  (`SnoiseTieScopeTests`, goldens computed by the 0.3.0 DLL). `snoise` is now
+  continuous across the diagonals to within 1e-4 over two ulps either side
+  (`NoiseGradTests`, `SnoiseIsContinuousOnTheSimplexDiagonal`). Anything keyed
+  on integer lattice coordinates (voxel or tile seeds, cell centres, generated
+  content sampled on a whole-number grid) changes; regenerate it when you take
+  this version.
 
 ### Added