Luminary Research Archive
Luminary Research ArchiveIndependent scholarship
Luminary Portal

All Research

Research

154 papers
Browse papers
  1. Spectral Crowding and Compression Limits for Arithmetic Covariance OperatorsScott SchubrEdition 2 · 2026-11-02 Public
  2. Diffusion budgets for contact-freezing lattice ellipsoidsScott SchubrEdition 2 · 2026-11-02 Public
  3. Stable star marginals and strict edge correlations for random forestsScott SchubrEdition 3 · 2026-11-02 Public
  4. Sharp output ranges and bias frontiers for stabilizer purity estimationScott SchubrEdition 2 · 2026-11-02 Public
  5. Covariance confidence bounds and parity certificates for stable count lawsScott SchubrEdition 3 · 2026-11-02 Public
  6. Log-concave polynomial prefix sums: algebraic certificates and a sharp zero sectorScott SchubrEdition 3 · 2026-11-02 Public
  7. Audibility of all odd blind modes in rapidly twisted polar-strip tubesScott SchubrEdition 3 · 2026-11-02 Public
  8. Sharp collision criteria for frozen color histogramsScott SchubrEdition 3 · 2026-11-02 Public
  9. Sharp noise transitions for an adaptive single-copy stabilizer-learning processScott SchubrEdition 3 · 2026-11-02 Public
  10. Leading bias and positive correction of heat-kernel Sinkhorn metricsScott SchubrEdition 3 · 2026-11-02 Public
  11. Chollet's inequality for positive semidefinite matrices of rank at most fourScott SchubrEdition 4 · 2026-11-02 Public
  12. Bose gases in weakly twisted annular-sector waveguidesScott SchubrEdition 3 · 2026-11-02 Public
  13. Optimal concavity powers for lattice counts on smooth toric Fano threefoldsScott SchubrEdition 3 · 2026-11-02 Public
  14. A square-integral threshold for subadditivity on shrinking corridorsScott SchubrEdition 5 · 2026-11-02 Public
  15. Small-ball estimates for Hölder centers of the Kloosterman processScott SchubrEdition 3 · 2026-11-02 Public
  16. Finite-projection holomorphic stabilization of contractible affine manifoldsScott SchubrEdition 4 · 2026-11-02 Public
  17. Power Concavity of Low-Dimensional Unimodular Fiber CountsScott SchubrEdition 5 · 2026-11-02 Public
  18. Positive Eigenfunctions Above the First Eigenvalue of the Affine 2-LaplacianScott SchubrEdition 4 · 2026-11-02 Public
  19. Finite Persistent Memory in Exact Sampling: Countable Rigidity and Algebraic Memory BoundsScott SchubrEdition 3 · 2026-11-02 Public
  20. Mixed-state escape bounds and proper agnostic learning of stabilizer states in odd-prime dimensionsScott SchubrEdition 4 · 2026-11-02 Public
  21. Resolving Goldreich's Open Problem 4.1: Linear Lower Bounds for Cubic Graph Isomorphism TestingScott SchubrEdition 7 · 2026-11-02 Public
  22. Eight-point fiber certificates and binary-input list recovery of folded Reed–Solomon codesScott SchubrEdition 3 · 2026-11-01 Public
  23. Single-time boundary heat-flux rigidity for smooth domainsScott SchubrEdition 4 · 2026-11-01 Public
  24. RH: Complete Signed Certificates and Canonical Null SynthesisScott SchubrEdition 12 · 2026-11-01 Public
PublicEdition 2

A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta product

Scott Schubr

Original PDF · First-page preview

Loading original first page…

Abstract

We give a complete rational reconstruction of an explicit obstruction to positive definiteness for a fixed-center product of the Riemann theta density. At s_0=(1)/(4)log(13/(4π)), the signed derivative functional evaluated on the square of P(X)=X^5-264X^3+10952X lies in the exact rational interval [-1412370791.837791749, -1412370791.837791748]. The proof constructs derivatives by formal power series, retains twelve theta summands, bounds the entire remaining series, and encloses exponentials by range-reduced alternating series. A printed table of rational moment intervals proves the negative contraction. The odd derivative Hankel block is indefinite, and the six-point translation Gram has a negative direction at every sufficiently small positive spacing.

Read the full paper in the original PDF.