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  1. Certified source elimination for localized odd Weil formsScott SchubrEdition 2 · 2026-10-27 Public
  2. Trace-perturbed minimizers of the mixed discriminantScott SchubrEdition 2 · 2026-10-27 Public
  3. Single-copy learning of noisy stabilizers by certified filteringScott SchubrEdition 2 · 2026-10-27 Public
  4. Exponential growth of sparse Euler products and normal graded domainsScott SchubrEdition 2 · 2026-10-27 Public
  5. Phase transitions and effective curvature bounds in Fourier density modelsScott SchubrEdition 2 · 2026-10-27 Public
  6. Sharp Stability and Geometric Classification of a Vámos Quartic DeformationScott SchubrEdition 2 · 2026-10-27 Public
  7. Strong permanent inequalities for cycles and a class of single-chord supportsScott SchubrEdition 2 · 2026-10-27 Public
  8. Sharp Quadratic Smoothing for Truncated Simplex SumsScott SchubrEdition 2 · 2026-10-27 Public
  9. Sharp limitations of two permanental cofactor comparisonsScott SchubrEdition 2 · 2026-10-27 Public
  10. Three-point positivity for weighted products of Riemann theta density powersScott SchubrEdition 2 · 2026-10-27 Public
  11. Strong permanent inequalities on three chorded seven-cycle supportsScott SchubrEdition 2 · 2026-10-27 Public
  12. Coupled permanent cofactors: sharp occupation bounds and compensation geometryScott SchubrEdition 11 · 2026-10-27 Public
  13. Strong permanent inequalities for three-row bipartite supports and triangle-free supports through order sevenScott SchubrEdition 2 · 2026-10-27 Public
  14. Strong permanent contraction on four-row bipartite supports through six columnsScott SchubrEdition 2 · 2026-10-27 Public
  15. Strong permanent contraction on four-by-seven bipartite supportsScott SchubrEdition 2 · 2026-10-27 Public
  16. Finite-order positivity and growing negative inertia for averaged Riemann theta productsScott SchubrEdition 2 · 2026-10-27 Public
  17. Row-dependent bounds for strong permanent contraction on four-by-eight supportsScott SchubrEdition 2 · 2026-10-27 Public
  18. Compact capture and protected bridges on the Koras–Russell cylinderScott SchubrEdition 2 · 2026-10-27 Public
  19. Dimension-dependent holomorphic certificate degrees on zero-sum hyperplanesScott SchubrEdition 2 · 2026-10-27 Public
  20. Admissible kernel lifts with positive endpoint forms and nonreal Fourier zerosScott SchubrEdition 2 · 2026-10-27 Public
  21. Global finite-depth stability and nonreal zeros of admissible Fourier transformsScott SchubrEdition 2 · 2026-10-27 Public
  22. A Weyl Law for Rapidly Twisted Polar-Strip TubesScott SchubrEdition 2 · 2026-10-27 Public
  23. Weighted polynomial localization and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  24. Weyl Laws and Angular Stability for Rapidly Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 3

Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theorem

Scott Schubr

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Abstract

We give a reproducible method for locating and certifying quintic obstructions for the normalized fixed-center Riemann theta product, and prove a unique transition in its odd quintic moment block on [3.64,3.66]. The transition parameter lies strictly between 3.64888758188562 and 3.64888758188563. For x∈ I=[3.64,3.66], below the transition, degree five is the minimum degree of a polynomial whose square has negative signed-moment value; at the transition the degree-five form is positive semidefinite with a one-dimensional nullspace; above it the form is positive definite. The proof combines a Schur-complement reduction with uniform directed interval bounds, including the complete infinite theta tails. An exact rational arithmetic replay verifies the bounds on the entire interval. An explicit integer-coefficient quintic illustrates why testing one fixed polynomial does not locate the transition of the full quintic block.

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