The tuned pass warned: 121/20000 differ, 6 over the bound, worst 1.72e-05, still 0
isosurface crossings. The port is fine; the bound was wrong.
It was 16 * max(|Old|, 1) * FLT_EPSILON — ULPs on the OUTPUT density. But density is
min(Z - Floor, Ceil - Z), so near the isosurface the output tends to 0 while the
intermediates are in the hundreds. Rounding born at scale ~400 judged against a
yardstick of scale 1: 400x too tight, and tightest exactly where the test looks
hardest. Large amplitudes are what expose it, which is why the tuned pass earned
its place immediately.
Measured rather than assumed: amplitudes rose x2.25-3.33 and the deltas rose x4.5,
with the worst delta at 0.345 ULP of |Z| — sub-ULP at the scale it is born in. Error
proportional to amplitude is ordinary rounding. A wrong noise offset or a missing
abs() would move the surface by voxels, four orders of magnitude above this.
The bound now scales with max(|Old|, |Z|, strate Z bounds), and the warning prints
the discriminator instead of just the alarm: the density at the offending sample and
the delta in ULPs of the working scale. A few ULP at near-zero density is
cancellation; thousands is drift. That distinction is now readable rather than
re-derivable at a build apiece.
The box verdicts held under the worst case: 32/60 proved uniform, 0 unsound, under
tripled ceiling roughness and 3x the columns — exactly the case that stresses the
Max(CeilZ - noise, FloorSurface + 2) clamp.
Also recorded in DECOMPOSITION section 3: FlatPlain and CrystalChamber render
identical in the live world because nothing in the content distinguishes them. The
merge loses no distinction; it reveals there was none.
UNVERIFIED: the corrected bound.
Co-Authored-By: Claude Opus 5 <noreply@anthropic.com>
Fr0zka
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