[jwr404]

Summary

Under the same gate p ≥ max(64, 4K + 2C) and 16 g ceil(log2 p) ≤ p,

2 g (9 p^2 + p^6 exp(-p^2))^{g-1} p^6 exp(K p - p^2) < 2^{-C p}

for integers p ≥ 2, g ≥ 1, K ≥ 0 and C ≥ 0. The approximant exponent without this factor is at most -C p - 4. The factor 2 is one bit, so the remaining slack is 3 and the exponent above is at most -C p - 3.

The base stays strictly below 16 p^2 because p^6 exp(-p^2) < 1/2 for p ≥ 64 and 9 p^2 + 1 < 16 p^2. This does not identify HALO's 2g rectangles with the tensor difference. The section ceiling and the section error stay hypotheses. At g = p^2 the monomial is still greater than 1. No new κ. The selected record remains 23/10000.

This answers the open question of #4497. It does not replay #4497. #4487 spends the same bit on the coefficient 10. One tensor axis is left open.

Test plan

• python3.12 -B scripts/research_package.py --package research/gaussian-tensor-nine-faces
• Prints PASS_GAUSSIAN_TENSOR_NINE_FACES and outcome=completed
• Maintainer replay was not run

Base 2a13eb1827784206202db90e5dc8327cf8a250db, priority revision 7. Upstream fetched at 2026-10-22T02:42:08Z was still that commit, and the pre-submit fetch was unchanged.

Prepared by James Reed with substantial Cursor Grok 4.7 assistance.