Datasets:

PureOne
/

QX-NEPHRIEL-Seventh-String

# Sources, attribution, and scope

Accessed 3 October 2026. Publication and posting dates are distinguished from access dates.

1. J. Chollet, "Is there a permanental analogue to Oppenheim's inequality?", American Mathematical Monthly 89 (1982), 57–58. DOI: 10.1080/00029890.1982.11995380. Original conjecture; historical metadata checked against the author-maintained survey below.

2. Yair Lavi, "Conjecture 30: Chollet's conjecture", author-maintained Minc's-list page. https://yair-lavi.com/mincs-list/conjecture-30/index.html . The retrieved page explicitly lists the complex rank-at-most-three result as covering every order except n=7. This is evidence of a documented gap, not proof that no other source has closed it. The page's claimed other results are not used to prove the order-seven theorem in this package.

3. Yicen Ma, "Quantitative Chollet Inequalities for Matrices of Rank at Most Four: Spectral bounds and an order-nine tight-frame construction", arXiv:2609.37461v1, posted 28 September 2026. https://arxiv.org/html/2609.37461v1 . In particular, the interpolated row bound and the complex-sphere / spectral-tilt estimates appear in its Sections 2 and 3. These are attributed ingredients, not discoveries claimed by this note. The present main proof specializes those bounds to rank three, eliminates the remaining two eigenvalues, and closes a scalar envelope by convexity and three rational endpoint bounds. The quoted paper's computer-assisted rank-four claims are not required by this main proof.

4. Jaikumar Radhakrishnan, "An Entropy Proof of Bregman's Theorem", Journal of Combinatorial Theory, Series A 77 (1997), 161–164. DOI: 10.1006/jcta.1996.2727. Author repository record: https://repository.ias.ac.in/57644/ . The binary-matrix entropy proof in PROOF.md is standard background and is attributed accordingly.

5. Qingfeng Li, Qirui Zhao, Wenhao Luo, "Chollet's Permanent Conjecture Through Order Six via Border Induction", Preprints.org 202608.2196, posted 31 August 2026. https://www.preprints.org/manuscript/202608.2196 . The retrieved page labels it a preprint that is not peer-reviewed. It supplies the small-order external theorem when forming the all-order rank-three corollary. The order-seven proof and the n>=7 appendix are independent of it.

## Novelty boundaries

The order-seven scalar certificate and the quantitative bounds were derived during this conversation. A targeted search did not locate the same stated 24/25 result. That search is not a complete priority audit. Several mathematical ingredients are explicitly existing results, and the result must not be marketed as the unrestricted Chollet conjecture being solved. No claim of independent peer review or Lean formalization is made.

## Computational trust boundaries

verify_q7.py checks the finite rational inequalities in the analytic order-seven proof and the n>=10 tail. verify_q8_q9.py supplies exact closed-interval coverage for two auxiliary orders. These programs do not mechanically prove the entropy bound, the spherical change of measure, or the analytic reductions. Those arguments are written out for mathematical review. Floating-point exploration suggested the closure but is not part of the proof certificate.
## Release source check (3 October 2026)
The current arXiv abstract/HTML and Preprints.org landing page were checked again when preparing this release. Their titles, authors, identifiers and posting dates agree with the records above. The Lavi progress page still explicitly reports the complex rank-three exception at order seven. Historical bibliographic metadata were corroborated by that bibliography and the author repository record; access to some publisher pages was restricted. This source check is a metadata and attribution check, not a mathematical audit of the cited preprints or a comprehensive priority search.

	# Sources, attribution, and scope

	Accessed 3 October 2026. Publication and posting dates are distinguished from access dates.

	1. J. Chollet, "Is there a permanental analogue to Oppenheim's inequality?", American Mathematical Monthly 89 (1982), 57–58. DOI: 10.1080/00029890.1982.11995380. Original conjecture; historical metadata checked against the author-maintained survey below.

	2. Yair Lavi, "Conjecture 30: Chollet's conjecture", author-maintained Minc's-list page. https://yair-lavi.com/mincs-list/conjecture-30/index.html . The retrieved page explicitly lists the complex rank-at-most-three result as covering every order except n=7. This is evidence of a documented gap, not proof that no other source has closed it. The page's claimed other results are not used to prove the order-seven theorem in this package.

	3. Yicen Ma, "Quantitative Chollet Inequalities for Matrices of Rank at Most Four: Spectral bounds and an order-nine tight-frame construction", arXiv:2609.37461v1, posted 28 September 2026. https://arxiv.org/html/2609.37461v1 . In particular, the interpolated row bound and the complex-sphere / spectral-tilt estimates appear in its Sections 2 and 3. These are attributed ingredients, not discoveries claimed by this note. The present main proof specializes those bounds to rank three, eliminates the remaining two eigenvalues, and closes a scalar envelope by convexity and three rational endpoint bounds. The quoted paper's computer-assisted rank-four claims are not required by this main proof.

	4. Jaikumar Radhakrishnan, "An Entropy Proof of Bregman's Theorem", Journal of Combinatorial Theory, Series A 77 (1997), 161–164. DOI: 10.1006/jcta.1996.2727. Author repository record: https://repository.ias.ac.in/57644/ . The binary-matrix entropy proof in PROOF.md is standard background and is attributed accordingly.

	5. Qingfeng Li, Qirui Zhao, Wenhao Luo, "Chollet's Permanent Conjecture Through Order Six via Border Induction", Preprints.org 202608.2196, posted 31 August 2026. https://www.preprints.org/manuscript/202608.2196 . The retrieved page labels it a preprint that is not peer-reviewed. It supplies the small-order external theorem when forming the all-order rank-three corollary. The order-seven proof and the n>=7 appendix are independent of it.

	## Novelty boundaries

	The order-seven scalar certificate and the quantitative bounds were derived during this conversation. A targeted search did not locate the same stated 24/25 result. That search is not a complete priority audit. Several mathematical ingredients are explicitly existing results, and the result must not be marketed as the unrestricted Chollet conjecture being solved. No claim of independent peer review or Lean formalization is made.

	## Computational trust boundaries

	verify_q7.py checks the finite rational inequalities in the analytic order-seven proof and the n>=10 tail. verify_q8_q9.py supplies exact closed-interval coverage for two auxiliary orders. These programs do not mechanically prove the entropy bound, the spherical change of measure, or the analytic reductions. Those arguments are written out for mathematical review. Floating-point exploration suggested the closure but is not part of the proof certificate.

	## Release source check (3 October 2026)

	The current arXiv abstract/HTML and Preprints.org landing page were checked again when preparing this release. Their titles, authors, identifiers and posting dates agree with the records above. The Lavi progress page still explicitly reports the complex rank-three exception at order seven. Historical bibliographic metadata were corroborated by that bibliography and the author repository record; access to some publisher pages was restricted. This source check is a metadata and attribution check, not a mathematical audit of the cited preprints or a comprehensive priority search.