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  1. Positive Operator Cocycles in Shrinking CorridorsScott SchubrEdition 2 · 2026-10-31 Public
  2. Coherence thresholds for optimal-rate stabilizer purity testingScott SchubrEdition 2 · 2026-10-31 Public
  3. Spectral escape for interacting and coalescing signed potential formsScott SchubrEdition 5 · 2026-10-30 Public
  4. Large negative subspaces for positive Euler deformationsScott SchubrEdition 3 · 2026-10-30 Public
  5. Fourier computation of empirical diffusion metricsScott SchubrEdition 2 · 2026-10-30 Public
  6. Purity frontiers and optimal copy complexity for qutrit stabilizer measurementsScott SchubrEdition 2 · 2026-10-30 Public
  7. Polynomial cores and inertia under Carleman moment boundsScott SchubrEdition 3 · 2026-10-30 Public
  8. Collision-uniform kernel asymptotics for Báez–Duarte zero packetsScott SchubrEdition 4 · 2026-10-30 Public
  9. Mixing-weight entropy concavity near the Gaussian below one-half signalScott SchubrEdition 3 · 2026-10-30 Public
  10. Covariance-Spectrum Certificates for Homogeneous Stable Count LawsScott SchubrEdition 8 · 2026-10-30 Public
  11. Relative tail payment and spectral enclosuresScott SchubrEdition 1 · 2026-10-29 Public
  12. Joint inclusion bounds for random greedy matroid basesScott SchubrEdition 1 · 2026-10-29 Public
  13. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  14. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  15. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  16. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  17. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  18. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  19. Exact-rank quadratic correlation: a phase-compatible Clique reductionScott SchubrEdition 1 · 2026-10-27 Public
  20. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  21. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  22. Independent Squares and Average-Radius Obstructions for Linear CodesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  24. A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta productScott 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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