← NS-X72 / X72-61 · Fast-Slow Stable Bundle Optimal Matching Exponent

NS-X72 · X72-61 Correction 2026-08

X72-61: Fast-Slow Stable Bundle Optimal Matching Exponent

Continuing from Round 60's ν^(-1/3) WKB boundary-layer scale, this round points out that if dichotomy roughness is applied directly at the originally proposed overlap point j_m=ν^(-1/4), the ratio of the slow-gap to the coefficient error reaches only O(1) — not enough to serve as a rigorous perturbation parameter. It decomposes the zero-viscosity three-dimensional minimal bundle exactly into two fast minimal lines plus one slow neutral line, thereby reducing the proof's dimension from three to one, and after rebalancing the three conservative error terms, obtains a corrected optimal overlap exponent α*=2/7, with matching-error target O(ν^(1/7)); six-dimensional Grassmannian principal-angle numerical diagnostics show the actual convergence is far faster than this conservative bound. This round does not prove a₃(ν)/ν→c₀; the gap shifts to STOP-C65 (the fast-Schur/slow-Riccati quantitative gap), left for the next round; this round includes numerical verification scripts and CSV data.

This round's status: Correction — 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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