# Verification report

The mathematical verification is the detailed analytic proof in main.tex
and the originating researcher's self-audit in reproducibility/proof_audit.md.
No independent review or formal verification is claimed.

The boundary proof establishes a full smooth ambient extension of the flat
holomorphic graph function; a compactly supported perturbation with globally
bounded Hessian; a regular, bounded, strongly convex negative sublevel set;
and the exact pullback identity rho(F_c(z)) = ||z||^2 - 1. The same identity
proves properness and transversality. Distinctness is checked at zero while
all boundary jets agree at p. The parameter circle is |c|^2 = Re(c), not
the unit circle.

The interior proof uses orthogonality of different homogeneous degrees on
the sphere and the nonnegative radial norm of qG-P. Boundary polynomial
norm equality forces that norm to tend to zero. No denominator lower bound
or rationality hypothesis on the comparison map is used.

The standard-library Python replay verifies 42 rational circle parameters,
231 cubic norm samples, 660 Whitney norm samples, 12 derivative recurrence
polynomials and one Hardy norm identity: 946 exact supplementary cases per
mode. All checks use explicit exceptions, and normal and optimized Python
must give identical output. Source hashes are additionally checked in the
local research dossier. The upload archive omits third-party PDFs and
explicitly skips only those source-hash checks.

These finite computations do not certify the infinite analytic assertions
or novelty. The general optimal interior order and the interior reading of
the second AIM bullet remain unresolved. The compiled package has a
separate build_record.json and visual_audit.json recording the actual
portable rebuild and all-page inspection.