# Verification report

Title: Weighted Root Deletions and Coefficientwise Toeplitz Positivity
Author: Alper Ferudun, Mercury Software GmbH
Date: 28 September 2026

## Mathematical acceptance

The explicit independent-weight theorem and its uD+v corollary have a
complete proof accepted after detailed self-audit. The accepted claim is
uniform in alphabet size, minor order and index gaps. Only the D+a branch
of AIM Problem 1.4 is closed; the whole multi-operator record is not solved.

The proof's critical obligations are the top-degree Schur-module
compression, the variable constant coefficient c_0=h, the LR width bound,
orthogonality of distinct remaining-letter contents, and nonnegative
exponents when root weights are separated. They are proved explicitly.
No independent reviewer or proof assistant has verified this manuscript.

## Exact computations

- verify_bordered.py: 9,629 assertions, including 4,257 whole Toeplitz
  polynomials, 46 rational trace identities, character orthogonality and
  dimensions through degree seven, star principal minors, and controls.
- verify_projection.py: 1,736 assertions; 34 complete symbolic polynomials
  and 146 nonzero coefficients are compared against actual projected-vector
  squared norms. Cross-layer orthogonality is checked directly.
- Both scripts passed on Python 3.13.5 and 3.12.14: 11,365 assertions per
  runtime. Exact integers and fractions only; no floating-point eigensolvers.
- Domains and source hashes are embedded in the four attached receipts.
  Different runtimes do not constitute independent mathematical review.

The universal result follows from the proof, not extrapolation from these
finite tests. Controls explicitly reject pointwise-to-coefficient inference,
positivity of arbitrary quotients, and removal of the grading hypothesis.

## Sources and novelty

Official AIM report, Sokal slides, classical Gram/projector and branching
sources, the prior anonymous affine release, and the later ribbon-Hadamard
preprint were checked at their relevant statements. The withdrawn Kim--Oh
claim is not used. Prior tools and the earlier affine theorem are credited.
Novelty remains bounded and uncertified; no absolute priority is claimed.

## Artifact checks

The standalone English source compiled successfully with the native desktop
LaTeX compiler. Tectonic export also succeeded after an approved missing-font
download. The earlier network failure is preserved in the research dossier.
Final PDF: six pages, 92,957 bytes, all six visually inspected with no
clipped formulas, overlap, broken glyphs or bad references. The final log
has no relevant compilation or typesetting warnings.

The byline contains only Alper Ferudun. Affiliation, email and GitHub are in
the author footnote. AI assistance is disclosed in ordinary prose.

## Publication state

Package ready, unpublished. No DOI has been reserved or registered for this
paper. No arXiv submission, site deployment or HF notice has been made.
The existing Zenodo file-access barrier is not bypassed; a public DOI must
be verified before a new EulerSolve listing or a source-accurate HF notice.