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  1. Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theoremScott SchubrEdition 3 · 2026-10-27 Public
  2. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  3. Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificatesScott SchubrEdition 3 · 2026-10-27 Public
  4. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
  5. Fekete convergence from balanced integer predecessors in shrinking corridorsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp trace-degree certificates for rank-two permanent-derivative compensationScott SchubrEdition 2 · 2026-10-27 Public
  7. Residual Certificates and Empirical Sharpness for Entropic Self-Transport ScoresScott SchubrEdition 2 · 2026-10-27 Public
  8. Observation norms under double-exponential confinementScott SchubrEdition 2 · 2026-10-27 Public
  9. Residual Stopping and Pointwise Inference for Nonuniform Entropic Self-TransportScott SchubrEdition 2 · 2026-10-27 Public
  10. Finite-spectral recovery of Weyl-blind twisting modesScott SchubrEdition 2 · 2026-10-27 Public
  11. Local comparison counting for linear extensions and a bounded-range balance refinementScott SchubrEdition 2 · 2026-10-27 Public
  12. An explicit hyperbolicity threshold for xi Jensen polynomialsScott SchubrEdition 2 · 2026-10-27 Public
  13. A quantitative Chollet inequality for rank-four matrices of order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Single-copy learning of stabilizers with correlated diagonal noiseScott SchubrEdition 2 · 2026-10-27 Public
  15. Relative finite optimization of arithmetic approximation distancesScott SchubrEdition 2 · 2026-10-27 Public
  16. Growing null subtraction and weighted Weil zero detectionScott SchubrEdition 2 · 2026-10-27 Public
  17. Frequency Localization for Weil Operator CertificatesScott SchubrEdition 3 · 2026-10-27 Public
  18. Sharp logarithmic sampling thresholds and lacunary interpolation in the Báez–Duarte step spaceScott SchubrEdition 2 · 2026-10-27 Public
  19. Joint Cutoffs and Negative-Spectrum Decay for Weighted Weil OperatorsScott SchubrEdition 3 · 2026-10-27 Public
  20. Sharp convergence of heat-kernel Sinkhorn metricsScott SchubrEdition 2 · 2026-10-27 Public
  21. Positive heat-flow observations on spherical shells: cutoffs, optimal preparation and concentrationScott SchubrEdition 2 · 2026-10-27 Public
  22. Curvature classification and certified Sinkhorn metrics for Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  23. Mean ergodic convergence from near-diagonal subadditivityScott SchubrEdition 2 · 2026-10-27 Public
  24. Quantitative Null-Space Compression for a Weighted Weil OperatorScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 7

Degree-eight positivity and polynomial obstructions for monotone Riemann theta averages

Scott Schubr

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Abstract

Monotone center averaging makes the complete Riemann theta product moment matrix positive definite through degree eight, under the corresponding moment-integrability hypothesis. The lower-degree conclusions retain their weaker hypotheses, and every finite physical parameter is included. The proof separates positive mean Schur residuals from variance reserves, with complete-theta tail and finite-interval certificates. This finite positivity has a quantitative extension but an all-order boundary. At every fixed degree N, the local moment Gram has a 99/100 reserve in normalized Hermite coordinates for X≥1000N^2. In contrast, every sufficiently large center cutoff admits negative rational polynomial squares in both parities, of degree at most ⌈ A^(31/4)⌉. At A=23/2, explicit witnesses have degrees 4096 and 4097, with certified complete-theta moment signs. Positive, strictly increasing bounded real-analytic center weights also yield negative polynomial squares. The local physical consequences include fixed configurations of at most nine points. Classical Schur, approximation and quadrature tools are identified as inputs; the complete-theta estimates, witnesses and quantitative domains are the results studied here.

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