fix(noise): variable-persistence's octave shift was an alias of ZERO - 1.8e-3 to 1.1e-5 (#162)

[wormeyman]

Second instance of the defect fixed in #166, found by taking that finding's own prediction seriously.

The finding

variablePersistenceMultioctaveNoise carried a fitted per-octave x shift of -7936. The basis lattice has period 256 per axis, and

-7936 = -31 * 256

so it names the same field as a shift of zero. The old comment's own warning about "false minima near -4864 / -3840" gives it away - those are -19*256 and -15*256. Every candidate the scan surfaced was a multiple of 256, which is what a completely flat fit direction looks like from the inside. The independence checks the notes were proud of (input-scale, seed, offset_x, persistence) could not discriminate either, because the period is independent of all of them.

VariablePersistenceMultioctaveNoise::run settles it: the octave loop reloads the x and y offsets from the same two constant slots (+0xa2c, +0xa30) on every iteration and has no counter-scaled term at all. Octaves decorrelate through lacunarity alone. OCTAVE_SHIFT is deleted, not set to 0.

Same pairing as #166, and here the mismatch is spectacular

variant	worst	f32-exact
f64 + shift -7936 (shipped)	1.847e-3	61/266
f64 + no shift	1.847e-3	61/266 — a literal no-op
f32 + shift -7936	3.629e-1	45/266 — 196x worse than doing nothing
f32 + no shift	1.144e-5	66/266 — 161x better

That third row is the sharpest illustration of why this class of bug hides: k*(-7936) at octave 5 lands near -39680, where an f32 ulp is ~3.9e-3. Anyone reproducing the game's arithmetic without first questioning the constant would conclude f32 was the wrong theory.

What is left is not a modelling gap

The remaining 1.1e-5 is basisNoise's f32 floor amplified by this op's 2^N × output_scale gain. worst/gain is 1.2e-7 to 2.4e-7 - one to two f32 ulps - in every one of the seven cases, including those with offset_x of 5000 and 40000. The spec now asserts that ratio per case as well as the absolute worst, so a regression that scales with gain can't hide inside a loose absolute bound.

Spec changes

The near-field/far-field split is gone along with the shift that motivated it - it thresholded on maxNoiseX(...) < 500 computed from k*(-7936) and allowed the far domain 100x more error. With no shift, the offset_x=40000 case is no worse than the ones at the origin.

Guards mirror #166: all three pre-fix models must still fail the tolerance.

No downstream statistic moved. pnpm run verify exits 0 (1736 passed).

🤖 Generated with Claude Code

https://claude.ai/code/session_01KTCpQXFZ79UoVGunewFyL7