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  1. Self-concordance and allocation for spatial power sumsScott SchubrEdition 3 · 2026-11-01 Public
  2. Sharp all-times heat-content comparison and concentration on compact metric graphsScott SchubrEdition 3 · 2026-11-01 Public
  3. Energy-Filtered Dynamical Localization in Constructive Dirichlet TowersScott SchubrEdition 3 · 2026-11-01 Public
  4. Degree-dependent minimax laws for Gaussian factorial momentsScott SchubrEdition 2 · 2026-11-01 Public
  5. A sharp lower bound for adjacent-edge correlations in random subtreesScott SchubrEdition 4 · 2026-11-01 Public
  6. Sharp transport identification with unknown Gaussian covarianceScott SchubrEdition 3 · 2026-11-01 Public
  7. Statistical inference for empirical heat-kernel Sinkhorn metricsScott SchubrEdition 5 · 2026-11-01 Public
  8. First-Hit Stopping and Bias-Corrected Score Inference in Dimension ThreeScott SchubrEdition 5 · 2026-11-01 Public
  9. Sharp Wasserstein Stability for Gaussian Deconvolution of Log-Concave LawsScott SchubrEdition 4 · 2026-11-01 Public
  10. Exact low-brightness minimax risk for quartic Gaussian energyScott SchubrEdition 1 · 2026-11-01 Public
  11. Sharp estimation costs for thermal Gaussian energies with known backgroundScott SchubrEdition 1 · 2026-11-01 Public
  12. Sharp calibration costs for high-order thermal Gaussian energiesScott SchubrEdition 1 · 2026-11-01 Public
  13. A sharp flatness transition for critical heat traces in twisted tubesScott SchubrEdition 1 · 2026-11-01 Public
  14. Prescribed-Gradient Coefficient Stability for Lorentzian PolynomialsScott SchubrEdition 1 · 2026-11-01 Public
  15. Closure correlations in paving and low-corank matroidsScott SchubrEdition 1 · 2026-11-01 Public
  16. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 4 · 2026-11-01 Public
  17. Polynomial inertia of signed measures with negative intervalsScott SchubrEdition 3 · 2026-11-01 Public
  18. Holomorphic certification on real subspacesScott SchubrEdition 3 · 2026-11-01 Public
  19. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 5 · 2026-11-01 Public
  20. Optimal unbiased Gaussian quantum estimation and the cost of unknown squeezingScott SchubrEdition 1 · 2026-11-01 Public
  21. Optimal unbiased estimation of polynomial energies in thermal Gaussian statesScott SchubrEdition 3 · 2026-10-31 Public
  22. Unrestricted Half-Power Obstruction and Polynomial Certificates for the Vámos QuarticScott SchubrEdition 5 · 2026-10-31 Public
  23. Dimension thresholds for log-concavity of normalized mixed momentsScott SchubrEdition 3 · 2026-10-31 Public
  24. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 2 · 2026-10-31 Public
PublicEdition 2

Real-section permanent-derivative compensation and quadratic phase control

Scott Schubr

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Abstract

We prove a uniform lower bound for a compensated homogeneous permanent derivative on the entire real centered positive semidefinite section of order six. If r is the trace, the bound is strictly greater than 5000r^4 for nonzero matrices, with explicit positive reserves from two actual omission variances. The proof cancels two signed contractions by subtracting fifty-eight times the fourth-degree omission variance and pays the ordinary side with the third-degree omission variance. No spectral gap, rank or entry-sign restriction is needed. Conjugation symmetry makes the loss along an imaginary perturbation quadratic; explicit coefficient and multilinear norm budgets then prove the lower bound 219r^4 on the closed complex tube ‖Im K‖_F≤ r/1000. We also record the unrestricted complex cancellation identity and its quadratic-state correction. Its remaining coupled remainder is not paid globally.

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