Proof / theorem Mathematics
Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theorem
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
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. Within this interval, 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.
Keywords Riemann theta density · moment matrices · positive definiteness · quintic obstruction · computer-assisted proof
Scope of the work
The minimum-degree and transition theorem is restricted to x ∈ [3.64, 3.66] for the normalized fixed-center product. Positive definiteness above the transition refers to the degree-five form, not the entire kernel. No conclusion about center-averaged kernels, global minimum degree, or the Riemann Hypothesis is drawn. The precursor remains at https://luminaryoddities.com/researcharchive/explicit-quintic-obstruction-riemann-theta-kernel (edition 1).
Reproduction notes
The reviewed October 17 publication package includes the exact manuscript, PDF, supplemental verification code, directed interval and exact rational certificates, source-only reproduction entrypoint, review records, and checksum manifest. A fresh source-only reproduction completed successfully before staging. Internal AI review records are not external human peer review.
The manuscript
Read the paper
The complete manuscript, as published in this edition.
If the reader is unavailable on your device, open or download the PDF directly.
Author disclosures
AI assisted derivation, verification code, and preparation; the author takes responsibility for the manuscript.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theorem (Version 1). Luminary Research Archive. https://luminaryoddities.com/researcharchive/locating-quintic-obstructions-riemann-theta-product/v/1
BibTeX
@techreport{luminary_locating_quintic_obstructions_riemann_theta_product_v1,
title = {Locating Quintic Obstructions in the Riemann Theta Product: A certified transition and minimum-degree theorem},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Proof / theorem},
note = {Version 1},
url = {https://luminaryoddities.com/researcharchive/locating-quintic-obstructions-riemann-theta-product/v/1}
}Reader correspondence
Share feedback
Questions, observations, and corrections are welcome. Your message goes privately to the research team and refers to edition 1.
Sign in with ChatGPT to send feedback