# Verification report

The complete counterexample is accepted by detailed self-audit of the
rank argument, apolar inverse-system duality, blockwise kernel formula,
all-subspaces bound and unique maximizing ideal. No mathematical gap
was found in the stated algebraically closed characteristic-zero scope.
No independent review or formal proof-assistant verification took place;
novelty and absolute priority are not certified.

Normal and optimized Python runs agree on 629 distinct subspaces for
m=1,...,4 and 1264 exact quotient-length calculations. The implementation
uses sparse polynomial differentiation and rational row reduction,
not the proved formula, to compute the actual lengths. Controls include
the explicit rank upper bound, concision, unique maximizing subspace,
two general-element selections, a nongeneral element giving an invalid
rank bound, and an excluded ideal with higher-degree generators.
An initial mixed-degree diagnostic overcount was fixed by taking a
basis across derivative layers; both final receipts were regenerated.
Finite diagnostics are not the proof over all subspaces.

Three retained primary-source PDFs and eleven complete relevant pages
were inspected. The degree-one-generated-ideal definition is explicit
in Definition 3.5 of the merged Carlini et al. paper. Known rank
additivity and the older noncomputable quartic are distinguished from
the present closure question. Third-party source PDFs are not included
in the distributable ZIP.

The package manifest and readiness receipt record the actual final
PDF visual audit and portable rebuild. This package is not yet a public
DOI record or a journal publication.