Occupation bounds for coupled permanent cofactors

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Subjects

Mathematics · Linear Algebra and Matrix Inequalities

Keywords

permanent inequalities, positive semidefinite matrices, coupled cofactors, occupation bounds, Gram factors, adaptive certificates

Manuscript date

2026-10-23

Reader reuse

No additional permission granted

Scope

The paper develops sharp all-order coupled permanent-cofactor residual bounds and occupation-resolved refinements for arbitrary complex positive semidefinite Gram matrices. Nonnegative variance, frame-variance bounds, trace-one operator formulations and conditional compensation domains retain the common Gram origin and allow singular limits. A self-contained reconstruction of the attributed small-order induction yields scalar inequalities through order six.

Disclosures

AI-assisted tools supported research exploration, literature review, manuscript preparation and internal verification. The author retains responsibility for the work. Internal AI-assisted and computational checks are distinct from external human peer review.

Reproduction

The exact publication package includes the 27-page manuscript, editable LaTeX sources, reader/build instructions, citation metadata, public checksums and any necessary mathematical or computational supplements. Keep its 17 members together and follow the included README for dependencies, build commands and any finite verification programs. Published finite checks support the stated analytic arguments.

References and related resources

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