Research Article · Preprint Mathematics
The Riemann Hypothesis through Arithmetic Weil Positivity
- Primary subject
- Mathematics
- Subject subfields
- Functional Analysis · Number Theory · Numerical Analysis
- Paper type
- Research Article
- Manuscript stage
- Preprint
- Manuscript
- Archived
- Edition
- 1 · Permanent link
Overview
Abstract
We give constructive cofinal criteria implying the Riemann hypothesis through complete signed inequalities in an original odd weighted Weil realization. For the actual arithmetic positive operator obtained by exponential cutoff averaging, we prove a complete origin-observation cap bounded by CΩ³(1 + log log M)³ at ridge 1/M, simultaneously for every 0 < Ω ≤ 1 and every finite exact constraint space. Thus width 1/log M has a vanishing actual receiving cap. A complementary-band criterion combines this theorem with full mixed covariance to return allowances tending to zero and hence RH. Positive gamma averaging preserves the minimal domain and supplies an explicit arithmetic remainder decreasing geometrically at a fixed seed. Local Sobolev inverse covariance, exact polar Green cancellation and a compact smooth preimage give the receiving estimate. Explicit mean and continuum-reference caps provide quantitative calibrations. Hard-cutoff common-receiver limits and intrinsic rank bounds accompany complete actual-positive energy-tail and true finite-head reductions. Conditioned polynomial complements and full covariance certificates give reproducible finite implementations.
Keywords Riemann hypothesis · Weil positivity · arithmetic receivers · cofinal criteria · uniform origin bounds · inverse covariance · certified operator bounds
Scope of the work
A complete origin-observation inverse bound for the actual averaged arithmetic positive operator, uniform over all profiles, every 0 < Ω ≤ 1 and finite exact constraints. The bound CΩ³(1 + log log M)³ vanishes for Ω = 1/log M. Exact mixed-covariance and complementary-band hypotheses give cofinal original-domain signed inequalities with vanishing allowances and imply RH. Gamma-smoothed arithmetic remainders, source-aware finite reductions and certified covariance constructions supply constructive implementations.
Reproduction notes
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Author disclosures
AI assistants supported derivation, literature comparison, manuscript preparation and independent checks. The author is responsible for the mathematical statements and presentation.
A stable scholarly record
Cite this edition
Scott Schubr. (2026). The Riemann Hypothesis through Arithmetic Weil Positivity (Version 1). Luminary Research Archive. https://research.luminaryoddities.com/riemann-hypothesis-arithmetic-weil-positivity/v/1
BibTeX
@techreport{luminary_riemann_hypothesis_arithmetic_weil_positivity_v1,
title = {The Riemann Hypothesis through Arithmetic Weil Positivity},
author = {Scott Schubr},
year = {2026},
institution = {Luminary Research Archive},
type = {Research Article},
note = {Version 1},
url = {https://research.luminaryoddities.com/riemann-hypothesis-arithmetic-weil-positivity/v/1}
}Loading discussion…