# Verification and scope report

The written proof establishes total nonnegativity for all minors by
positive-bidiagonal approximation and finite Cauchy--Binet sums. Entire
inverse and determinant one are direct. Exact entry asymptotics prove
regularity. A Jordan trace-parity argument, together with a strict trace
crossing for all noncommuting positive phases, rules out every entire
complex logarithm. Proportional generators prove the converse.

The originating researcher's self-audit found no remaining gap in this
stated theorem. This is not independent peer review or proof-assistant
verification. The mathematical result is not inferred from finite sampling.

The retained Python checker passes 58,624 exact rational assertions on
Python 3.12 and 3.13. The independent Node implementation passes 951
assertions using scalar path convolution and recursive Leibniz
determinants, including all 923 nonempty minors of a 6 by 6 window.
The Python implementation instead convolves folded coefficients and
uses rational elimination. The checks overlap; two runtime replays
are not counted as two independent algorithms.

The explicit r=4 Jordan witness and -1/12 block-truncation minor are
checked without floating point. The complete analytic theorem and
the all-minor limit argument remain written proofs.

The counterexample targets Lemma 8.4 of arXiv:0812.0840v3. The journal
version was not obtained. The known failure of a single holomorphic
logarithm and the Kutzschebauch--Studer upper bound are credited.
Novelty of this regular two-phase classification is undetermined;
no priority certification is implied by the bounded literature search.
The whole original AIM factorization question remains unresolved.

Final manuscript compiler, exported PDF and full-page visual QA receipts
are retained in the publication checkpoint. A successfully built package
does not itself mean that a DOI or external publication already exists.