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2025
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| Online Access: | https://doi.org/10.5281/zenodo.19410041 |
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| _version_ | 1866902084381573120 |
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| author | Hanners, Michael |
| author_facet | Hanners, Michael |
| contents | <p>This manuscript presents the formalization and proof of Hanners Theorem, establishing the existence of discrete eigenstates and finite nonzero mass gaps in non-Abelian gauge theories via an entropy-minimization framework termed Harmonic Coherence (HC). The argument proceeds in two complementary tracks—gauge-theoretic and information-theoretic—that converge: the spectral mass gap is the gauge-theoretic manifestation of the entropy gap established by the fixed-point theorem.</p><p>Three principal results are established: fixed-point existence for the HC evolution map, convergence to a normally hyperbolic invariant manifold, and identification of HC fixed points as natural Condition C sources with sub-Shannon compression. Applications to seven Millennium-class problems, cosmological resolutions, and a universal scaling law are developed in the main body and companion papers.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19410041 |
| institution | Zenodo |
| language | |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Hanners Theorem Formalization: Information-Theoretic Foundations of Harmonic Coherence Hanners, Michael Hanners Theorem Harmonic Coherence entropy minimization non-Abelian gauge theory mass gap fixed-point existence Condition C sub-Shannon compression normally hyperbolic invariant manifolds spectral theory quantum confinement mathematical physics <p>This manuscript presents the formalization and proof of Hanners Theorem, establishing the existence of discrete eigenstates and finite nonzero mass gaps in non-Abelian gauge theories via an entropy-minimization framework termed Harmonic Coherence (HC). The argument proceeds in two complementary tracks—gauge-theoretic and information-theoretic—that converge: the spectral mass gap is the gauge-theoretic manifestation of the entropy gap established by the fixed-point theorem.</p><p>Three principal results are established: fixed-point existence for the HC evolution map, convergence to a normally hyperbolic invariant manifold, and identification of HC fixed points as natural Condition C sources with sub-Shannon compression. Applications to seven Millennium-class problems, cosmological resolutions, and a universal scaling law are developed in the main body and companion papers.</p> |
| title | Hanners Theorem Formalization: Information-Theoretic Foundations of Harmonic Coherence |
| topic | Hanners Theorem Harmonic Coherence entropy minimization non-Abelian gauge theory mass gap fixed-point existence Condition C sub-Shannon compression normally hyperbolic invariant manifolds spectral theory quantum confinement mathematical physics |
| url | https://doi.org/10.5281/zenodo.19410041 |