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  1. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  2. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
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  9. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
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  13. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  15. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  17. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  18. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  19. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  20. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  21. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  22. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  24. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Uniform permanent-derivative compensation on the six-row conjugate-disjoint Gram locus

Scott Schubr

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Abstract

We prove a uniform lower bound for a compensated homogeneous permanent derivative on the complete conjugate-disjoint locus of centered complex positive semidefinite matrices of order six. The locus has rank at most two, and the theorem includes arbitrary phases, nonuniform diagonals, unequal eigenvalues and singular limits. If r is the trace, p the product of the two possible nonzero eigenvalues and δ the ordinary omission variance, the lower bound is [1248 − (1672/3)√2]r⁴ + [29568 − (33920/3)√2]pr² + (20160 − 80√2)δ. All three coefficients are positive. The proof extends the earlier rank-one cancellation identity before imposing spectral relations, then uses an exterior-square Gram identity to pay the coupled remainder with the same variance reserve. Combined with an earlier conditioning-free projection and explicit Lipschitz estimate, this gives a uniform small-overlap region in the full centered positive semidefinite section.

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