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  1. Critical-tail localization and growing theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  2. Pure-Point Dirichlet Spectrum in an Enlarging Cube TowerScott SchubrEdition 2 · 2026-10-27 Public
  3. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  4. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  5. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  6. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  7. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  8. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  9. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  10. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  11. All-depth root-Laguerre positivity with nonreal Fourier zerosScott SchubrEdition 3 · 2026-10-27 Public
  12. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  13. Sharp degree exponents for polynomial detection of isolated negative atomsScott SchubrEdition 2 · 2026-10-27 Public
  14. A sixth-order obstruction to total positivity of an arithmetic theta trace kernelScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp collision laws and subexponential masking for polynomial certificatesScott SchubrEdition 2 · 2026-10-27 Public
  16. Collision geometry and concentration in polynomial sign recoveryScott SchubrEdition 2 · 2026-10-27 Public
  17. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  18. Growing-Index Recovery and Tail Scales for Signed MeasuresScott SchubrEdition 2 · 2026-10-27 Public
  19. A Positive Corner Limit for Inverse Half-Powers of Vámos QuarticsScott SchubrEdition 2 · 2026-10-27 Public
  20. A counterexample and corrected translation-density criterion for correlation kernelsScott SchubrEdition 2 · 2026-10-27 Public
  21. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
  22. Exact minimax estimation of homogeneous complex Gaussian energiesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit global lower certificate for a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  24. Odd Weil-form bounds by positive exterior eliminationScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 3

Strong Self-Permanent Inequalities for Complex Four-Row Bipartite Supports

Scott Schubr ORCID

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Abstract

The paper proves a strong self-conjugate permanent inequality for every complex positive semidefinite matrix whose off-diagonal support is bipartite with one part of size at most four. The permanent of its entrywise squared modulus is bounded by its permanent times the product of its diagonal entries. The other part has arbitrary finite size, so the result permits unbounded matrix order and arbitrary complex cycle phases. The proof combines a matching-polytope overlap bound with a column-independent endpoint argument and a large-entry reduction. A five-by-five extension, proved by an exact polynomial certificate, gives the same strong inequality for every bipartite support through total order ten. A separate total-energy estimate gives the ordinary self-Chollet inequality on every positive semidefinite bipartite support with one part of size at most twelve. Complete analytic reductions and portable exact verification are supplied.

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