# Verification report

Problem: AMR-021-0014, the weighted Forsgård–Shapiro coefficient-parity conjecture, final-journal Shapiro2015 Section7 Conjecture9.

Result: an explicit degree1,000,077 polynomial with every coefficient positive and rational, exact weighted parity count1, and at least3 distinct negative real roots. The compact factorial/exponential prefix is defined symbolically, not approximated by zero coefficients. No optimal degree or exact total root count is claimed.

The manuscript contains the complete source-scoped argument: strictly negative prefix quantities and boundary, exact shifted local signs, both selected parity blocks, and a uniform perturbation bound preserving four exact rational seed signs. The printed appendix was executed unchanged with exact rational arithmetic; root additionally checked440 finite prefix identities. The symbolic proof, rather than a million-coefficient numerical array, covers every prefix index.

The seed is the previously public unweighted degree77 note (DOI10.5281/zenodo.23050917), cited and restated. Related global tropical counterexamples of Forsgård–Novikov–Shapiro are credited separately. No inspected prior exact weighted resolution was located in the bounded primary-source comparison; historical firstness is not certified.

The author heading contains only Alper Ferudun. Mercury Software GmbH, email and GitHub appear in a footnote. AI assistance is disclosed in the body prose. This is a self-audited, AI-assisted, unrefereed preprint, not independent human refereeing or formal proof-assistant verification.

The native LaTeX compiler reported success. The final source was also exported with the already installed engine, with no TeX warnings, and the four pages were checked for readable mathematics, references, code, margins and author layout. Hash-bound QA and exact certificates accompany the source package. No third-party full-text binaries are redistributed.