# Verification of the binary octic decomposition count

The six-page English preprint proves that a general complex binary octic has 76 decompositions into three fourth powers of quadratic forms modulo permutations and independent fourth-root rescalings. The ordered affine map degree is 29184; quotienting only by permutations gives 4864. The complete theorem treats (k,d)=(4,2), not the entire perfect-pair problem.

## Proof and prior work

The proof projects the third secant of the quartic Veronese surface to binary octics. Landsberg and Ottaviani provide the established degree 112 and the scheme-theoretic middle-catalecticant equations. The calculation determines the actual projection base as a ribbon on a rational quartic, with nilpotent ideal O(-4). The normal-bundle computation gives the correction 112 - 64 + 28 = 76. Dominance, generic reducedness and uniqueness of three-term ternary decompositions justify interpreting the intersection number as a count of actual decompositions.

Kowalczyk and Vill previously obtained the number 76 numerically and used restriction to a conic. Both are credited. The contribution is the geometric derivation, not discovery of the numerical value. Their inspected arXiv v2 is cited exactly. A bounded primary-source search found no earlier proof of this ribbon correction; this is not an exhaustive novelty or priority certificate. No conclusion about real decompositions or a closed-form construction of every summand is asserted.

## Exact algebraic checks

The portable SymPy checker in reproducibility/check_identities.py was executed both normally and with Python optimization. Both executions passed and produced identical JSON output. It checks:

- All six Schur polynomials printed in the appendix against the actual matrix.
- Both ideal inclusions over Q: four reductions in one direction and six in the other.
- The five explicit support-cover minor identities.
- The reduced-coordinate and nilpotent-coordinate transitions on the chart overlap.
- The rank-six smoothness Jacobian and its displayed determinant.
- The nonzero derivative determinant of the nine-dimensional Waring map.
- All 540 matrix entries obtained by directly differentiating the fifteen ternary quartic monomials.

The program uses explicit error checks, not Python assertions that disappear under optimization. Its checks do not replace the cited geometric theorems or the argument passing from intersection degree to generic cardinality. The exploratory specialized-fiber calculations are not premises of the generic proof and are not needed to run this package.

## Manuscript and package checks

The current source compiled successfully with the desktop editor's native LaTeX compiler. The publication PDF was exported with the installed Tectonic compiler; its retained log has no warnings, unresolved references, overfull boxes or underfull boxes. All six final page images were inspected. Formulas, matrices, references, footnote and page boundaries were legible without clipping or overlap.

Only Alper Ferudun appears on the author line. Mercury Software GmbH, the professional email and GitHub link are in its footnote. AI assistance is disclosed in ordinary prose, not under a separate heading. Source and public metadata are English. Package manifests bind the final artifacts and the source ZIP members by SHA-256; third-party PDFs, frozen dataset extracts, private coordination files and credentials are excluded.

## Verification boundary

Acceptance is based on the originating researcher's detailed self-audit and the explicit written proof. The work is unrefereed, not independently reviewed, and not formalized in a proof assistant. The source problem remains unresolved outside the stated pair. A ready package is not evidence of DOI registration or public release; those stages require separate repository, website and announcement receipts.