← NS-X72 / X72-62 · Neutral Residual Cancellation and the Quarter-Power Matching Law

NS-X72 · X72-62 Refinement 2026-08

X72-62: Neutral Residual Cancellation and the Quarter-Power Matching Law

Continuing from Round 61's approach of compressing the error budget into a fast-Schur graph and a slow-Riccati part (STOP-C65), this round examines the remainder that actually acts along the neutral direction after Schur elimination, proving that the neutral residual cancels exactly down to S_n=48K³/n³+O(n⁻⁴) (rather than the originally estimated O(n⁻²)), so the neutral-root drift is only cubic order, and derives the asymptotic viscous-coupling corrections 1+j⁻¹ and 1+2j⁻¹ for the two parities. On this basis it rebalances the three post-Schur error terms, correcting the optimal overlap exponent from Round 61's 2/7 back to α*=1/4, restoring the "quarter-power matching law" as a structurally self-consistent theorem target; the six-dimensional principal-angle numerics remain far better than this conservative bound even at ν=10⁻⁸. This round still does not prove the full O(ν^(1/4)) theorem; the gap shifts to STOP-C66, left for the next round to construct an explicit invariant fast graph; this round includes numerical verification scripts and CSV data.

This round's status: Refinement — Taken from the file's own objective/executive-result section, meaning preserved, not a full verbatim translation.

Connections

Relationship to the rest of the series, stated as closely as possible in the document's own words, not my interpretation.

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