# Verification report

Accepted scope: p_n^+=p_n for every n>=1, with a rank-preserving two-sided Perron-ray identity for every nonzero matrix of finite cp-plus-rank. The proof applies to singular matrices. The separate maximum pointwise-gap question and a numerical formula for general p_n are outside the result.

The written proof and detailed originating-researcher self-audit are included in the source archive. No known mathematical gap remains in this theorem. Bomze-Dickinson-Still's positive Perron lift and interior ray theorem are credited, not presented as new. The bounded source search does not certify absolute priority. Independent review and proof-assistant verification have not occurred.

Exact Fraction regression passed for 240 positive factors (94 singular Gram matrices), 720 negative-ray steps, 720 rank-preservation checks and 60 upward sparse-factor steps. The checker rejected 1,443 deliberately invalid variants. Ordinary Python, optimized Python and a second Python runtime produced byte-identical reports. These are formula/hypothesis tests, not computations of minimal cp ranks or a substitute for the general proof.

The built-in LaTeX compiler and the exported PDF compilation succeeded. All four PDF pages were visually inspected; no clipping, overlapping text, unresolved references or malformed mathematical notation was found. The title shows the author's name only; affiliation and contact details are in a footnote, and AI assistance is disclosed in running prose.

The source archive contains standalone LaTeX, original proof/audit notes, portable checker code and outputs. It does not redistribute third-party PDFs. Hashes and source URLs are retained separately. The paper is ready for an unrefereed release; no Zenodo deposit, DOI, site publication or HF notice is claimed by this report.