The Maximal Finite CP-Plus-Rank Equals the Maximal CP-Rank
Manuscript 13 October 2026 · Online 13 October 2026
Abstract
The cp-plus-rank is the smallest number of columns in a strictly positive Gram factor. We prove that, in every order \(n\), its largest finite value equals the maximal cp-rank \(p_n\). A strictly positive factor stays positive under a sufficiently small contraction along the Perron eigendirection. Together with the positive Perron lift of Bomze, Dickinson and Still, this realizes every finite cp-plus-rank as an ordinary cp-rank in the same order and matrix rank, including singular matrices.
This determines the relation between the two maxima, not a numerical formula for \(p_n\) or the maximum pointwise gap. The AI-assisted preprint is self-audited and unrefereed; no absolute priority, independent review or formal verification is claimed.
Record
- Affiliation
- Mercury Software GmbH
- Contact
- [email protected] · GitHub
- Result
- Complete scoped theorem
- Categories
- math.OC · math.RA
- Manuscript
- 13 October 2026
- Online release
- 13 October 2026
- Version
- 1.0
- License
- Creative Commons Attribution 4.0 International
Files and verification
The PDF is the canonical reading copy. The source archive contains the LaTeX manuscript, bibliography, reproducibility material, and audit documents without build artefacts.
Citation
Alper Ferudun, “The Maximal Finite CP-Plus-Rank Equals the Maximal CP-Rank,” EulerSolve Research Papers, OWR-15957-003, 2026. https://doi.org/10.5281/zenodo.23350364.
BibTeX
@misc{ferudun2026cpplusrank,
author = {Ferudun, Alper},
title = {The Maximal Finite CP-Plus-Rank Equals the Maximal CP-Rank},
year = {2026},
howpublished = {EulerSolve Research Papers},
url = {https://eulersolve.org/papers/owr-15957-003/},
doi = {10.5281/zenodo.23350364},
note = {OWR-15957-003; unrefereed preprint}
}