← NS-X72 / X72-54 · Two-Sided Minimal Floquet Matching and Fredholm Defect

NS-X72 · X72-54 Numerical Evidence 2026-08

X72-54: Two-Sided Minimal Floquet Matching and Fredholm Defect

Building on Round 53's conclusion that 'a complete analytic rescue must select the minimal branch,' this round restores both the even and odd viscous coupling channels simultaneously, proves that the full six-step frozen recursion is a reciprocal sextic equation with no root on the unit circle for any positive viscosity, splitting exactly into three growing and three minimal reciprocal solutions. Redoing the physical finite truncation with the original divergence-free Fourier coefficients (free of representational redundancy), it stably exhibits two localized source-hidden modes and two localized adjoint-kernel modes, and Round 51's complete second-order source target has a stable nonzero projection onto them; under normalized viscosity, the minimal range-defect on the two source fibers stabilizes at about 0.965 and 0.994, respectively. Route halts at STOP-C58 (local-adjoint Fredholm / infinite-matching-proof gap): these figures are for now only truncation-stable numerical evidence, not yet upgraded to an infinite-dimensional theorem, handed to the next round to construct the infinite adjoint minimal solution and prove the matching is genuinely nonzero; this round also includes a numerical-verification script.

This round's status: Numerical Evidence — 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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