Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

135 papers
Browse papers
  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

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

Scott Schubr

Original PDF · First-page preview

Loading original first page…

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.

Read the full paper in the original PDF.