# Verification of the signed Grushin construction

The originating researcher completed a detailed mathematical self-audit of the form domain and core, spectral bounds, constrained gap, Bessel obstruction, angular identity, and passage to arbitrary smooth tests. The full proof is in main.tex; the step-by-step audit is in reproducibility/proof_audit.md.

Exact arithmetic verifies three universal total-derivative identities, nine trial/constant checks, 1001 angular sign regressions, and 64 rational parameter regressions. Normal and optimized interpreter outputs agree. These checks do not prove the analytic existence and convergence statements.

The desktop LaTeX compiler and Tectonic both compile the manuscript. All six final rendered pages were visually inspected; no clipping, missing formulas, unresolved references or layout defects were observed. Author and affiliation follow the requested name/footnote presentation. AI assistance is disclosed in prose.

This is a complete proof of the stated signed-weight counterexample, not an independent review, a formal proof-assistant verification, a novelty certificate, or a claim that every variant of the original source problem has been closed. The portable-build receipt accompanies the final package manifest.