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  1. Divisor tests and coefficient transfers for sextic character momentsScott SchubrEdition 1 · 2026-10-28 Public
  2. Strong Self-Permanent Inequalities for Complex Four-Row Bipartite SupportsScott SchubrEdition 3 · 2026-10-28 Public
  3. The Riemann Hypothesis through Arithmetic Weil PositivityScott SchubrEdition 4 · 2026-10-28 Public
  4. Signed Frequency Certificates and Constraint Costs for Odd Weil FormsScott SchubrEdition 1 · 2026-10-27 Public
  5. Uniform Resolvent Asymptotics for Growing Theta-Null Source FamiliesScott SchubrEdition 1 · 2026-10-27 Public
  6. Resolving Goldreich's Open Problem 4.1: Linear Lower Bounds for Cubic Graph Isomorphism TestingScott SchubrEdition 6 · 2026-10-27 Public
  7. Frequency-Source Resolvent Limits and Positive-Receiver InstabilityScott SchubrEdition 1 · 2026-10-27 Public
  8. Arithmetic cutoff bounds and sharp tail capacity for local Nyman–Beurling certificatesScott SchubrEdition 4 · 2026-10-27 Public
  9. Source-Resolved Resolvent Growth under Reciprocal-Theta ConfinementScott SchubrEdition 1 · 2026-10-27 Public
  10. Distributional traces and central moment tests for Vámos quarticsScott SchubrEdition 1 · 2026-10-27 Public
  11. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 1 · 2026-10-27 Public
  12. Exact-rank quadratic correlation: a phase-compatible Clique reductionScott SchubrEdition 1 · 2026-10-27 Public
  13. Sharp output ranges and bias frontiers for stabilizer purity estimationScott SchubrEdition 1 · 2026-10-27 Public
  14. Certified resolvent detection of the third Weyl-blind twisting harmonicScott SchubrEdition 2 · 2026-10-27 Public
  15. Degree-eight positivity and polynomial obstructions for monotone Riemann theta averagesScott SchubrEdition 7 · 2026-10-27 Public
  16. Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codesScott SchubrEdition 2 · 2026-10-27 Public
  17. Independent Squares and Average-Radius Obstructions for Linear CodesScott SchubrEdition 2 · 2026-10-27 Public
  18. An explicit quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  19. A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta productScott SchubrEdition 2 · 2026-10-27 Public
  20. Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theoremScott SchubrEdition 3 · 2026-10-27 Public
  21. Polynomial Recovery and Masking under Weak Exponential TailsScott SchubrEdition 2 · 2026-10-27 Public
  22. Finite positivity and correction inertia for the Riemann theta formScott SchubrEdition 2 · 2026-10-27 Public
  23. Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificatesScott SchubrEdition 3 · 2026-10-27 Public
  24. Collision and cancellation spectra for concentrated energy formsScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 3

Minimum-Degree Obstructions in the Riemann Theta Product: Classification, transition bounds and robust Gram certificates

Scott Schubr

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Abstract

We classify the least degree of a polynomial whose square has negative signed-moment value for the normalized fixed-center Riemann theta product. On 3≤ x≤12 the degree has fourteen transitions, takes values between five and fifteen, and is nonmonotone. We isolate every transition and determine the degree at equality. Jacobi symmetry extends the complete classification to π^2/12≤ x≤12. We quantify how the two- and three-summand theta models shift all fourteen crossings: the respective root errors are below 0.00049 and 2.588 × 10^(-10). A constructive finite-difference bound converts polynomial obstructions into finite translation Gram witnesses. Twenty explicit rational certificates include a seven-point example stable under absolute entrywise errors of 1.94 × 10^(-7). We also prove fixed-degree Gaussian limits and single-summand degree-five positivity. Infinite tails, directed interval covers and independent rational checks are included in a self-contained reproduction supplement.

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