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Critical Threshold and Double-Exponential Obstruction for Phase-Uniform Weil Certificates

Year: 2026

Type: article

Abstract: This note studies phase-uniform proof architectures for Weil positivity through Paley–Wiener compression operators. For the finite prime polynomial Pθ,aP_{\theta,a}, it introduces the operator critical threshold Ccrit(a)C_{\rm crit}(a) defined by the condition that the compressed positive-part operator remain within the 4a4a budget uniformly over all admissible prime phases. The main result is the explicit two-sided estimate (1−εa)A(a)≤Ccrit(a)≤A(a),(1-\varepsilon_a)A(a) \le C_{\rm crit}(a) \le A(a), with A(a)=2∑n<e2aΛ(n)n∼4ea,A(a)=2\sum_{n

Source: Zenodo (CERN European Organization for Nuclear Research)

DOI: 10.5281/zenodo.22864233

Author: umihara, hideo

Language: English

Topic: Analytic Number Theory Research

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7213783436

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