Statistical Rigidity of Wigner-Dyson Eigenvalue Distributions in Gaussian Unitary Ensembles: The Spectral Integrity Operator and Selberg Automorphic Stabilization
Abstract
Definition and exact evaluation of the Spectral Integrity Operator for Gaussian Unitary Ensemble (GUE) random matrices. Proves the identity T(E/I) = 1.000000 by combining the Wigner surmise normalization with the Dyson-Mehta spectral rigidity statistic at the James Arthur truncation scale. Establishes Selberg automorphic stabilization of stochastic time series onto the critical line Re(s) = 1/2. ⚖️ PROPRIETARY SOVEREIGN RESEARCH LICENSE (PSRL v2.0) © 2026 Dimitar Prodromov / AETERNA Technologies EOOD, Pomorie, Bulgaria. ALL RIGHTS RESERVED. ORCID: 0009-0004-8070-1348 | Architect ID: 101327948 GRANT OF LIMITED LICENSE: This work is published under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (CC BY-NC-ND 4.0) with the following additional legally binding restrictions constituting the Proprietary Sovereign Research License (PSRL v2.0): ACADEMIC PEER-REVIEW ONLY: Academic and scientific peer-review verification, citation, and scholarly commentary are strictly permitted under fair use/fair dealing provisions of applicable copyright law (Berne Convention, Art. 10; TRIPS Agreement, Art. 13; EU Directive 2019/790, Art. 3-5). PROHIBITION OF COMMERCIAL EXPLOITATION: Any unauthorized commercial exploitation, industrial implementation, commercial product development, financial instrument derivation, or revenue-generating application of the mathematical methods, algorithms, formulas, or computational architectures described herein is STRICTLY PROHIBITED without an explicit, bilateral, written commercial license deed executed by the copyright holder. PROHIBITION OF PATENT CLAIMING: Filing of any patent, utility model, or industrial design application that incorporates, derives from, or is substantially similar to the intellectual content of this work is EXPRESSLY FORBIDDEN and constitutes willful infringement under 35 U.S.C. §§ 271-273, European Patent Convention Art. 52-57, and Bulgarian Patent Law (ЗПРПМ, чл. 6-10). PROHIBITION OF AI/ML TRAINING: Ingestion, indexing, vectorization, embedding, fine-tuning, or any form of machine learning model training (including but not limited to large language models, diffusion models, and reinforcement learning systems) on the text, formulas, or data contained in this work is STRICTLY PROHIBITED without explicit written authorization. This prohibition is asserted under EU AI Act (Regulation 2024/1689), Art. 53(1)(c) opt-out; EU DSM Directive 2019/790, Art. 4(3) opt-out; and DMCA § 1202 (integrity of copyright management information). PROHIBITION OF DERIVATIVE WORKS: Creation of derivative works, translations, adaptations, abridgments, compilations, or transformative uses is PROHIBITED under the ND (NoDerivatives) clause of CC BY-NC-ND 4.0 and reinforced by Berne Convention Art. 12. DMCA / EU ENFORCEMENT: Any unauthorized reproduction, distribution, or public communication of this work will be subject to immediate DMCA takedown (17 U.S.C. § 512), EU Copyright Directive enforcement (Directive 2001/29/EC, Art. 8), and civil damages claims under Bulgarian Copyright Law (ЗАПСП, чл. 94-95) with statutory damages up to 100,000 BGN per infringement plus disgorgement of profits. MORAL RIGHTS: The author's moral rights of attribution (paternity) and integrity are inalienable and perpetual under Berne Convention Art. 6bis, Bulgarian ЗАПСП чл. 15-16, and French Code de la propriété intellectuelle L121-1. GOVERNING LAW: This license shall be governed by and construed in accordance with the laws of the Republic of Bulgaria, with exclusive jurisdiction vested in the District Court of Burgas (Окръжен съд — Бургас). For international disputes, the WIPO Arbitration and Mediation Center, Geneva, shall have supplementary jurisdiction. VIOLATION NOTICE: Any party found to be in breach of these terms will be subject to immediate legal action, including injunctive relief, statutory and actual damages, attorney fees, and criminal prosecution where applicable under national intellectual property criminal statutes.