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  1. Finite certificates for the lower edge of a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  2. Effective Prescribed-Gradient Stability for Homogeneous Real-Stable PolynomialsScott SchubrEdition 2 · 2026-10-27 Public
  3. Prescribed-gradient minimizers and coefficient stability for homogeneous real-stable polynomialsScott SchubrEdition 4 · 2026-10-27 Public
  4. Finite theta interpolation and eventual Laguerre failureScott SchubrEdition 2 · 2026-10-27 Public
  5. Uniform permanent-derivative compensation on the six-row conjugate-disjoint Gram locusScott SchubrEdition 2 · 2026-10-27 Public
  6. Certified complementary bounds for an odd Weil receiverScott SchubrEdition 1 · 2026-10-27 Public
  7. RH, Approximately: Certified Lower Bounds for Odd Weil PositivityScott SchubrEdition 1 · 2026-10-27 Public
  8. Sharp regularity criteria for arithmetic cutoff functionalsScott SchubrEdition 1 · 2026-10-26 Public
  9. Optimal energy for Dirichlet repairs in divisor bandsScott SchubrEdition 1 · 2026-10-26 Public
  10. Certified negative-band approximation for odd Weil formsScott SchubrEdition 1 · 2026-10-26 Public
PublicEdition 2

Strong permanent contraction on four-by-seven bipartite supports

Scott Schubr

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Abstract

We prove that every complex positive semidefinite matrix A supported in K_(4,7) satisfies per(|A|^2)≤per(A)∏_i a_(ii). The normalized off-diagonal block is a four-by-seven operator contraction. The new argument retains third-order minor contributions and controls their coupled phase cancellations through the row Gram matrix. A split according to the smallest squared row norm separates an analytic corner reduction from a balanced-row polynomial inequality. The latter is verified by an exact rational tensor Bernstein certificate on 256 boxes. An established all-column large-entry theorem covers the complementary region. The computer-assisted result includes arbitrary phases, missing edges and singular endpoints.

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