a-classical-proof-of-the-riemann-hypothesis-via-self-adjoint-spectral-theory
Formal repository for “A Classical Proof of the Riemann Hypothesis via Self-Adjoint Spectral Theory” by Lawrence Ip. Contains manuscript and philosophical context via the Spectral Unity Theorem.
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Formal repository for “A Classical Proof of the Riemann Hypothesis via Self-Adjoint Spectral Theory” by Lawrence Ip. Contains manuscript and philosophical context via the Spectral Unity Theorem.
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README.md
A Classical Proof of the Riemann Hypothesis via Self Adjoint Spectral-Theory
Author: Lawrence Ip
DOI (Zenodo Preprint): 10.5281/zenodo.15454540
Date of Preprint Release: May 18, 2025
🧠 Summary Overview
This manuscript presents a complete, self-contained proof of the Riemann Hypothesis (RH) grounded in spectral operator theory. The result is obtained through the explicit construction of a real, self-adjoint differential operator whose spectrum corresponds precisely to the imaginary components of the nontrivial zeros of the Riemann zeta function.
The proof is analytic, non-circular, and rigorously structured. It avoids heuristic reasoning or probabilistic analogies. Instead, RH is resolved as a necessary consequence of spectral identity and coherence saturation.
🔬 Core Result
The central achievement is the realization of a mathematically natural operator whose spectral structure inherently encodes the nontrivial zeros of the Riemann zeta function. The potential term in this operator is composed of a bounded harmonic field, a Gaussian-smeared arithmetic profile derived from the distribution of primes, and their convolution.
The construction guarantees self-adjointness, spectral completeness, and excludes the possibility of extraneous or off-critical eigenvalues. This confirms the Riemann Hypothesis as a structural identity condition within the spectral framework, rather than a standalone conjecture.
📐 Technical Domains
Spectral theory and operator analysis
Functional analysis and self-adjointness criteria
Harmonic analysis and trace formulas
Spectral density alignment with known zeta zero distributions
Foundations of Spectral Ontology
🔭 Philosophical Context
The proof is situated within the broader framework of Spectral Ontology, which recasts truth, identity, and mathematical existence in terms of coherence rather than axiomatics. Under this paradigm, the Riemann Hypothesis is not an open problem but a resolved structural effect of spectral closure.
This marks a unification point between arithmetic, analysis, and foundational logic—realized through the principle of coherent identity.
📜 License
This repository and its contents are licensed under the
Creative Commons Attribution 4.0 International License (CC BY 4.0).
You are free to share and adapt the material for any purpose, including commercial use, provided appropriate credit is given.
Owner
- Name: Lawrence Ip
- Login: nodepunk
- Kind: user
- Location: Melbourne, Australia
- Company: nodepunk
- Website: https://lawrenceip.info
- Twitter: lawrenceip
- Repositories: 7
- Profile: https://github.com/nodepunk
Architect and Operator of Spectral Coherence.
Citation (CITATION.cff)
cff-version: 1.2.0 message: "If you use this repository, please cite it as below." authors: - family-names: "Ip" given-names: "Lawrence" title: "A-Classical-Proof-of-the-Riemann-Hypothesis-via-Self-Adjoint-Spectral-Theory" version: 1.0.0 doi: 10.5281/zenodo.15454540 date-released: 2025-05-24 url: "https://github.com/nodepunk/A-Classical-Proof-of-the-Riemann-Hypothesis-via-Self-Adjoint-Spectral-Theory"
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