[jwr404]

Question

#4490 uses ||B - P|| < p^6 exp(-p^2) on one core axis. Does a core row kept at distance A = ceil(p^{48}) from every face lie past the within-cell agreement radius of #4452?

Result

Let p ≥ 2 and 0 ≤ W ≤ p - 1. The bandwidth R = (2 p^{24} - 1) W satisfies R < p^{26}, because

p^{26} - (2 p^{24} - 1)(p - 1) = p^{24} ((p - 1)^2 + 1) + p - 1 > 0.

For an integer p, A = p^{48}, and p^{48} = p^{26} p^{22} with p^{22} ≥ 2^{22} > 1. Thus R < p^{26} < A. The core row is strictly outside that bandwidth, so its section-polynomial row is the global polynomial row. Under the #4452 gauge, ||P - H_sec^{-1}||_2 < p^6 exp(-p^2).

Distance p^{25} fails: at p = 2 the loose radius is 2^{25} + 1.

Claim type: one distance comparison. No new κ. The ideal gaps stay hypotheses, and the operator bound is not re-proved. The #4100 notes still use p^{10} exp(-p^2).

The locality audit already says A clears the written radius for J = ceil(p^{42}). This comparison is against the lowered radius p^{26}.

This branch starts from canonical main. It does not replay #4452.

Test plan

python3.12 -B scripts/research_package.py --package research/gaussian-core-row

PASS_GAUSSIAN_CORE_ROW and outcome=completed on this machine. Maintainer replay has not been run.

Base 2a13eb1827784206202db90e5dc8327cf8a250db, priority revision 7, selection refresh κ = 23/10000.

Prepared by James Reed with substantial Cursor Grok 4.7 assistance.