Occupation bounds for coupled permanent cofactors

Scope of the work

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. The generic rank-six compensation inequality and unrestricted Chollet conjecture remain open.

Reproduction notes

The exact publication package includes the 28-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 arguments; they do not replace universal analytic proofs or establish external human refereeing.

Author 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.

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