# Verification report

The manuscript provides a complete analytic proof for all real exponents 0<s<1. The detailed self-audit checks the circular-mean inequality, uniform polygonal quadrature, kernel normalization and tail bound, strict first-variation exclusion, outer-boundary topology, positive capacity, and stability under thickening.

The standard-library Fraction checker passes 129 exact rational parameter certificates and 2020 auxiliary concavity inequalities in both ordinary and optimized execution, with identical JSON output. These checks validate sufficient bounds and arithmetic, not the universal analytic theorem.

The original report and BHS paper have been inspected, with six relevant complete local source pages reviewed visually. The 2009 review's conjecture was additionally read through public web extraction; its two unsuccessful local download routes are preserved in the research dossier and are not counted as downloaded PDFs. Literature comparison credits the existing axial reduction, scaling limit and domination method. The final package manifest binds the complete proof and source comparison.

This is detailed self-audit, not independent peer review or proof-assistant verification. No absolute novelty or priority claim is certified. Publication status is UNPUBLISHED; an unassigned DOI must not be displayed as registered.