# Verification report for the balanced Laurent potential note

The accepted mathematical scope is complete: two exact filling-set
counterexamples to Theorem 4.7 of Ishibashi arXiv:2603.14338v2, a general
constant-adjoining mechanism, and a positive orbit-sum replacement with a
coercivity and Hessian proof in arbitrary finite dimension. The logarithmic
sum has a separate covariance-Hessian proof. General infinite-group
properness is outside the proved scope; the AIM record is not counted closed.

The printed source definitions and theorem were read and the critical PDF
page was visually checked. All five archived PDFs, their extracted texts,
and the recovered AIM page agree with the source manifest. Positive
INTEGRAL Laurent coefficients, slope-span, full-dimensional interior,
finiteness, and the global chart are explicitly checked in the proof audit.

check_exact.py passed 16,154 checks in Python 3.13.5 and 3.12.14. It uses
integer sparse Laurent identities and rational samples, including the five
pentagon identities and the earlier braid-scope calculations.
check_potentials.py passed 205 checks in both runtimes using separately
aggregated coefficients, exact moment and covariance matrices, and negative
controls. Repeating the same program in another runtime is not independent
mathematical review. The general theorem rests on the written proof, not
these finite samples.

The native LaTeX compiler successfully checked the final source. The
publication PDF was exported using already-installed cached Tectonic, and
all five rendered pages were visually inspected. No final-log undefined
references, overfull boxes or compilation warnings were observed. An initial
cached-font failure, fixed by an ordinary seed label, is preserved internally.

The proof was accepted by the originating researcher after detailed
self-audit. Independent human review and proof-assistant verification have
not occurred. Ishibashi's finite-subgroup fixed-point conclusion, the A2
cluster structure and the elementary convex-analysis ingredients are
credited as prior work. The bounded literature search establishes no
absolute-priority guarantee. Publication or DOI assignment does not change
these mathematical or review-status limitations.