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  1. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  2. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  3. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  4. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  5. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  6. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  7. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  8. Spectral escape and mean crossover for concentrating signed potential formsScott SchubrEdition 2 · 2026-10-27 Public
  9. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  10. All-depth root-Laguerre positivity with nonreal Fourier zerosScott SchubrEdition 3 · 2026-10-27 Public
  11. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  12. Sharp degree exponents for polynomial detection of isolated negative atomsScott SchubrEdition 2 · 2026-10-27 Public
  13. A sixth-order obstruction to total positivity of an arithmetic theta trace kernelScott SchubrEdition 2 · 2026-10-27 Public
  14. Sharp collision laws and subexponential masking for polynomial certificatesScott SchubrEdition 2 · 2026-10-27 Public
  15. Collision geometry and concentration in polynomial sign recoveryScott SchubrEdition 2 · 2026-10-27 Public
  16. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 2 · 2026-10-27 Public
  17. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  18. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 2 · 2026-10-27 Public
  19. Power Concavity of Low-Dimensional Unimodular Fiber CountsScott SchubrEdition 4 · 2026-10-27 Public
  20. Growing-Index Recovery and Tail Scales for Signed MeasuresScott SchubrEdition 2 · 2026-10-27 Public
  21. A Positive Corner Limit for Inverse Half-Powers of Vámos QuarticsScott SchubrEdition 2 · 2026-10-27 Public
  22. A counterexample and corrected translation-density criterion for correlation kernelsScott SchubrEdition 2 · 2026-10-27 Public
  23. Polynomial Certificates for the Vámos Riesz ObstructionScott SchubrEdition 3 · 2026-10-27 Public
  24. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratum

Scott Schubr

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Abstract

We study a homogeneous compensated derivative arising from permanent inequalities for centered complex positive semidefinite matrices of order six. On the conjugate-disjoint locus K K̄=0, the ordinary omission variance has exactly forty trace-normalized zeros, all sparse rank-one cube-root configurations. On the entire flat, equal-spectrum rank-two stratum, including all compatible complex phases, we determine the compensated derivative explicitly and prove its sharp lower bound 18912-140√2. The proof retains the common Gram structure: a real balanced-frame complement gives a complete complex-structure chart, and threefold permutation symmetry eliminates the remaining phase from the paired permanent derivative. An explicit Frobenius tube of radius 10^(-6) has a positive uniform margin and contains full-dimensional families of centered rank-five matrices, whose positive rank-one anchors have rank six. A conditioning-free positive-part construction also reduces small conjugate overlap to the exact locus.

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