diff --git a/packages/cultmath/tests/CultMath.Tests/SnoiseTieScopeTests.cs b/packages/cultmath/tests/CultMath.Tests/SnoiseTieScopeTests.cs
index 4f76edd3..8bf7c895 100644
--- a/packages/cultmath/tests/CultMath.Tests/SnoiseTieScopeTests.cs
+++ b/packages/cultmath/tests/CultMath.Tests/SnoiseTieScopeTests.cs
@@ -10,8 +10,8 @@ namespace CultMath.Tests;
 // set and its float32 band (below) the results are bit-identical to 0.3.0. The goldens below were computed by the
 // cultmath-unity-v0.3.0 tag's CultMath.dll (Runtime/Plugins), not by this code. Float32 rounding
 // decides whether a given integer-difference input ties, because x0 is computed in float32: an
-// input whose differences round onto whole numbers can tie too and move, within about one float32
-// spacing of the coordinate magnitude (a band that widens with the magnitude), and some inputs on
+// input whose differences round onto whole numbers can tie too and move, within a few float32
+// ulps of the largest coordinate (a probe found up to about two; the band widens with the magnitude), and some inputs on
 // the set keep their value (about 3% of random integer points). Every input below ties and moves
 // all five outputs (value and the four gradient words).
 // TieSetNow pins what this code returns on the same inputs, so that each of the two tie-rule sites
diff --git a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
index 0c64d105..2cb099ce 100644
--- a/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
+++ b/packages/cultmath/unity/org.gamecult.cultmath/CHANGELOG.md
@@ -23,9 +23,9 @@ backfilled here; see `docs/semver-policy.md` for why.
   value; measured over random integer points, about 97% change. The cell offset
   is computed in float32, so an input whose differences `y - x` and `z - x`
   round, in float32, onto whole numbers can tie and change too. How far from the set that
-  reaches grows with the coordinates' magnitude, at about one float32 spacing of the
-  coordinate (1.9e-6 at 30, 6.1e-5 at 1000, 7.8e-3 at 1e5; a probe over random inputs
-  never found a changed one farther than that). Computed coordinates such as `i * 0.1f`
+  reaches scales with the coordinates' magnitude: a few float32 ulps of the largest
+  coordinate (a probe over random inputs found changed inputs up to about two ulps
+  away; measured, not proved). Computed coordinates such as `i * 0.1f`
   can land there, so near large coordinates the band is wide. Elsewhere the results are
   bit-identical to 0.3.0 (`SnoiseTieScopeTests`, goldens computed by the 0.3.0
   DLL). `snoise` is now