# Verification report

Theorem: The first Artin cone for sextics in six variables is nonconvex.
Two disjoint Motzkin forms have quadratic SOS multipliers individually,
but their sum has minimum SOS multiplier degree exactly four. There are
also positive-definite counterexamples for sufficiently small perturbations.

The mathematical proof is complete within that scope and was audited by
the originating researcher. It is not independently refereed or formally
verified. The other optimization questions in OWR-13941-002 remain unresolved
by this work; no whole-record closure is claimed.

The self-contained proof checks the Motzkin non-SOS obstruction by cubic
coefficient elimination, then restricts any proposed quadratic multiplier
to zeros in each variable block. Lowest homogeneous parts force the
multiplier to vanish on a basis, which forces a quadratic SOS multiplier
to be zero. The quartic upper certificate is an exact twelve-square identity.

The checker uses only Python's standard library and exact integer/rational
arithmetic. Both normal and optimized runs pass with identical outputs:
two quadratic identities, one twelve-square quartic identity, six coefficient
eliminations, rank-six linear and rank-seven affine zero certificates, and
15,625 finite smoke tests. The finite samples are not the proof of the
universal statement. Run `python3 reproducibility/verify.py --output audit.json`
with a fresh output path. The script deliberately refuses to overwrite audits.

The positive-definite extension uses a proved closedness lemma, not numerical
experimentation. No explicit perturbation threshold is supplied.

The manuscript compiles with the built-in LaTeX compiler and Tectonic.
The final four pages were visually inspected. A separate source-archive
build and both exact-check modes are required by the package readiness
record. File hashes, source provenance and acceptance evidence bind the
released artifact. No third-party source PDFs are included in this package.