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  1. Critical-tail localization and growing theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  2. Pure-Point Dirichlet Spectrum in an Enlarging Cube TowerScott SchubrEdition 2 · 2026-10-27 Public
  3. Sharp permanent-derivative compensation on the flat equal-spectrum conjugate-disjoint Gram stratumScott SchubrEdition 2 · 2026-10-27 Public
  4. Geometric Blind Modes in the Weyl Asymptotics of Twisted TubesScott SchubrEdition 2 · 2026-10-27 Public
  5. Variance cancellation and two-direction bounds for six-row permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  6. Heat-Trace Recovery of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  7. Real-section permanent-derivative compensation and quadratic phase controlScott SchubrEdition 2 · 2026-10-27 Public
  8. Full-phase permanent-derivative compensation under real-part spectral pinchingScott SchubrEdition 2 · 2026-10-27 Public
  9. Phase-boundary reduction and low-rank compensation for permanent derivativesScott SchubrEdition 2 · 2026-10-27 Public
  10. Typical-value anchors for polynomial approximation and theta correction inertiaScott SchubrEdition 2 · 2026-10-27 Public
  11. All-depth root-Laguerre positivity with nonreal Fourier zerosScott SchubrEdition 3 · 2026-10-27 Public
  12. Polynomial synthesis and zero ideals for the Riemann xi-functionScott SchubrEdition 2 · 2026-10-27 Public
  13. Sharp degree exponents for polynomial detection of isolated negative atomsScott SchubrEdition 2 · 2026-10-27 Public
  14. A sixth-order obstruction to total positivity of an arithmetic theta trace kernelScott SchubrEdition 2 · 2026-10-27 Public
  15. Sharp collision laws and subexponential masking for polynomial certificatesScott SchubrEdition 2 · 2026-10-27 Public
  16. Collision geometry and concentration in polynomial sign recoveryScott SchubrEdition 2 · 2026-10-27 Public
  17. Left-Sector Mellin Certification of a Weyl-Blind Twisting ModeScott SchubrEdition 2 · 2026-10-27 Public
  18. Growing-Index Recovery and Tail Scales for Signed MeasuresScott SchubrEdition 2 · 2026-10-27 Public
  19. A Positive Corner Limit for Inverse Half-Powers of Vámos QuarticsScott SchubrEdition 2 · 2026-10-27 Public
  20. A counterexample and corrected translation-density criterion for correlation kernelsScott SchubrEdition 2 · 2026-10-27 Public
  21. Asymptotically optimal bounds for permanental cofactor matricesScott SchubrEdition 2 · 2026-10-27 Public
  22. Exact minimax estimation of homogeneous complex Gaussian energiesScott SchubrEdition 2 · 2026-10-27 Public
  23. An explicit global lower certificate for a weighted Weil operatorScott SchubrEdition 2 · 2026-10-27 Public
  24. Odd Weil-form bounds by positive exterior eliminationScott SchubrEdition 2 · 2026-10-27 Public
PublicEdition 2

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

Scott Schubr

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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.

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