Soul (cut 2a-i, pass 2) found two defects in cellular's own math.cs source
and its HLSL mirror:
- cellular hashed pcg3d/pcg4d over the FLOAT32 BIT PATTERN of each
integer-valued cell coordinate (pcg3d(neighbor), pcg4d(float4(cellId, 0)))
instead of the integer coordinate itself. Two adjacent cells' bit patterns
share more structure (same exponent, mantissa one increment apart) than
the integers do going into pcg3d's own mixing, and that structure survived
into the jitter: measured chi-square 203.8 for jitter.x over 1,000,000
cells against 15 degrees of freedom (critical value 37.7). Both call sites
now hash int3(neighbor)/int4(int3(cellId), 0) directly, in C# and in the
HLSL mirror (both shaders/CultMath.hlsl and the Unity copy, byte-identical
as before). This changes cellular's noise output — nothing has shipped, so
that is acceptable, but it is a real behavioural change, not a comment fix.
- The F6 exactness proof's "near-side neighbour" bound was wrong as written:
picking the near-side neighbour on a FIXED axis is not always within
sqrt(3) of the query (counterexample: u = (0.5, 0, 0) with the x-neighbour
jittered to (-1, 1-2^-24, 1-2^-24) gives ~2.06, past the radius-2
exclusion). The comment is rewritten to the correct argument: choose the
axis whose u_i sits closest to a cell boundary (m = min(u_i, 1-u_i) <=
1/2 on that axis), and the near-side neighbour on THAT axis has squared
distance at most (1+m)^2 + 2*(1-m)^2 = 3 - 2m + 3m^2 <= 3 on [0, 1/2],
strictly below 3 since the jitter never reaches the boundary. Margin
2 - sqrt(3) ~= 0.268 (Soul's adversarial check: worst in-box F2 is exactly
sqrt(3), only in the unattainable corner limit).
Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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