MeasureLipschitz on e89fd687 (Yggdrasil): sampled 7.1933103, refined 7.2400064,
x 1.10 = 7.9640074, witness (229.92526, 73.37927, -66.14595). The old 9.181147
sat on the diagonal tie. C#, both Interval.hlsl copies, the pin test's witness
and design.md's provenance numbers move together; CultMath.glsl follows with the
regenerated fixture.
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
The radius gains (|c|_1 + radius) 2^-20 in C# and both HLSL copies; the
doc's strictness claim leaves. TileBallEnclosesEveryRaySegment measures in
double over the r2 domain and seven extreme families with outward corner
flows, pins the radius two-sided, and counts misses per family. The noise
ball enclosure tests draw radii to 1e3.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
One new function in C# and both tracked HLSL copies (one blob): the centre on the
tile's central ray at mid-depth, radius ((z1 - z0) / 2) |(m_c, 1)| + z1 N / (sqrt(2) f)
+ warp. TileBallEnclosesEveryRaySegment checks 2,000 seeded tiles x 64 points
(sub-pixel corners at both depth ends with full-length flows) with no tolerance,
and pins the ball to the derivation so a grown ball fails too. The mirror's
compared-function count moves from 52 to 53.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
The cut's negative check is a pattern over math.Interval.cs and CultMath.Interval.hlsl: the
bounds use values only, so neither file names the gradient functions. Comments only.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
math.Interval.cs and shaders/CultMath.Interval.hlsl (included from CultMath.hlsl after Phacelle;
both tracked copies) add iv_point, iv_add, iv_sub, iv_neg, iv_mul, iv_scale, iv_abs, iv_min,
iv_max, iv_sqr, iv_sqrt, iv_exp, iv_clamp, iv_saturate, iv_smoothstep, iv_lerp, iv_snoise_ball
and iv_fbm_ball, and SNOISE_LIPSCHITZ = 10.099261 (1.10 x the refined max |snoise_grad| that
NoiseBoundTests.MeasureLipschitz prints). iv_exp and iv_smoothstep widen by one ulp through
asfloat(uint), added beside asuint as the HLSL intrinsic. The mirror test now compares 52
functions; the Unity package and the NuGet content files carry the new include.
Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>
