Research Article · Preprint Mathematics
Odd Weil-form bounds by positive exterior elimination
- Primary subject
- Mathematics
- Subject subfields
- Analysis and Spectral Theory · Number Theory and Special Functions
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 2 · Permanent link
Overview
Abstract
We give a complete lower certificate for the odd part of the original minimal theta-weighted Weil form. A positive infinite-rank exterior is absorbed through its directional covariance with the signed low-frequency features. An endpoint chord for the resolvent of the positive exterior reduces the required information to two finite matrices, without assuming a positive lower bound for the true feature Gram. At arithmetic cutoff eight this yields q_H[h] ≥ −1.88 × 10^(-9) ||h||₂² (h in the original form domain V, odd). The proof retains the original polar constraint, four odd exact derivative-null rows, the complete arithmetic remainder and all low/exterior mixed terms. Directed ball arithmetic verifies the resulting matrix of order 4085. The method also has a concrete boundary: at arithmetic cutoff eleven, with the same frequency band and multiplication parameter, the actual positive exterior has odd ambient norm greater than 1.7. We prove optimality of the first-moment resolvent bound in its finite information class and a convergent higher-moment refinement.
Keywords Weil form · theta function · operator lower bounds · Schur complement · directed ball arithmetic · spectral certificates
Scope of the work
The original minimal theta-weighted Weil form has odd-sector lower bound −1.88 × 10^(-9) in its specified norm. Directional positive exterior elimination preserves all mixed terms; at cutoff eleven the corresponding ambient odd exterior norm exceeds 1.7.
Reproduction notes
The 16-page manuscript and editable sources are supplied in 28 outer ZIP members, including three NPZ containers with four finite float64 arrays. README.txt and reproducibility/README.txt give Tectonic build commands and Python 3.12/NumPy 2.3.5/python-flint 0.9.0 dependencies. run_reproduction.py supplies scalar controls, saved-data replay and fresh regeneration modes. Replay reuses authenticated source enclosures; fresh mode regenerates primitive quadratures, full source sums, features and the 4085-row finite witness. The manuscript supplies the analytic/domain arguments.
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AI assistance was used in mathematical development, literature comparison, manuscript preparation and computational verification.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). Odd Weil-form bounds by positive exterior elimination (Version 2). Luminary Research Archive. https://research.luminaryoddities.com/odd-weil-form-bounds-positive-exterior-elimination/v/2
BibTeX
@techreport{luminary_odd_weil_form_bounds_positive_exterior_elimination_v2,
title = {Odd Weil-form bounds by positive exterior elimination},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 2},
url = {https://research.luminaryoddities.com/odd-weil-form-bounds-positive-exterior-elimination/v/2}
}Loading discussion…