Replication and Reproducibility Study · Preprint Mathematics
A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta product
- Primary subject
- Mathematics
- Subject subfields
- Number Theory and Special Functions
- Paper type
- Replication and Reproducibility Study
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
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.
Keywords Riemann theta density · positive definite functions · Hankel matrices · rational interval arithmetic
Scope of the work
A distinct rational reconstruction of the fixed-center quintic theta-product obstruction, including twelve retained summands, a complete tail bound, a printed rational moment contraction and small-spacing finite translation-Gram indefiniteness.
Reproduction notes
The paper has 6 pages. The editable-source archive contains 8 files. Compile main.tex with proof.tex. Standard-library supplement/verify_reconstruction.py freshly reconstructs the rational moments, complete tail and printed contraction.
The manuscript
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The complete manuscript, as published in this edition.
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A stable scholarly record
Cite this edition
Scott Schubr. (2026). A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta product (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/independent-rational-reconstruction-quintic-theta-obstruction/v/2
BibTeX
@techreport{luminary_independent_rational_reconstruction_quintic_theta_obstruction_v2,
title = {A rational reconstruction of a quintic obstruction for a fixed-center Riemann theta product},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Replication and Reproducibility Study},
note = {Version 2},
url = {https://research.luminaryoddities.com/independent-rational-reconstruction-quintic-theta-obstruction/v/2}
}Loading discussion…