The Critical Auto-Duality Conjecture: Numerical Evidence and Analytic Necessity
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901799845232640 |
|---|---|
| author | Coppi, Franck |
| author_facet | Coppi, Franck |
| contents | <p>The Critical Auto-Duality Conjecture (CADC) reformulates the Riemann Hypothesis by positing that the critical line Re(s) = 1/2 is the unique fixed locus of the functional-equation involution s ↦ 1−s. A non-circular discrete Hamiltonian defined on the logarithmic ladder of primes reconstructs the first 100 non-trivial zeros with a mean absolute error of 2.1 × 10^{-4}. Multi-layered evidence is presented, including spectral trace mismatch inequalities, minimal variance conjectures, symmetry breaking violating the Selberg trace formula, small-scale deviations from GUE statistics, thermodynamic divergence of the heat trace, non-existence of a well-defined infinite operator off the line, and failure of coherent non-circular regularization. Numerical simulations of the accumulated phase reveal a robust positive logarithmic drift on the critical line. Independent topological (Fredholm index logarithmic divergence) and informational (Beurling superior density saturation) obstructions further exclude off-critical configurations. While the infinitesimal gap δ(t) → 0 remains formally open, the convergence of these independent arguments strongly supports the critical line as the unique stable configuration compatible with spectral rigidity, arithmetic capacity, and informational consistency. CADC does not constitute a complete proof of the Riemann Hypothesis but provides one of the most comprehensive structural and empirical frameworks to date, making RH appear increasingly inevitable.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18664695 |
| institution | Zenodo |
| language | eng |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Critical Auto-Duality Conjecture: Numerical Evidence and Analytic Necessity Coppi, Franck Riemann Hypothesis, zeta function, explicit formula, Jacobi operator, discrete spectral model, Selberg trace formula, GUE pair correlation, heat trace, Agmon wells, Kato-Rellich, zero-free regions, ψ(x) error bounds, Carlson theorem, Hardy spaces, Weyl law, holomorphic rigidity, CADC, arithmetic operator, spectral rigidity <p>The Critical Auto-Duality Conjecture (CADC) reformulates the Riemann Hypothesis by positing that the critical line Re(s) = 1/2 is the unique fixed locus of the functional-equation involution s ↦ 1−s. A non-circular discrete Hamiltonian defined on the logarithmic ladder of primes reconstructs the first 100 non-trivial zeros with a mean absolute error of 2.1 × 10^{-4}. Multi-layered evidence is presented, including spectral trace mismatch inequalities, minimal variance conjectures, symmetry breaking violating the Selberg trace formula, small-scale deviations from GUE statistics, thermodynamic divergence of the heat trace, non-existence of a well-defined infinite operator off the line, and failure of coherent non-circular regularization. Numerical simulations of the accumulated phase reveal a robust positive logarithmic drift on the critical line. Independent topological (Fredholm index logarithmic divergence) and informational (Beurling superior density saturation) obstructions further exclude off-critical configurations. While the infinitesimal gap δ(t) → 0 remains formally open, the convergence of these independent arguments strongly supports the critical line as the unique stable configuration compatible with spectral rigidity, arithmetic capacity, and informational consistency. CADC does not constitute a complete proof of the Riemann Hypothesis but provides one of the most comprehensive structural and empirical frameworks to date, making RH appear increasingly inevitable.</p> |
| title | The Critical Auto-Duality Conjecture: Numerical Evidence and Analytic Necessity |
| topic | Riemann Hypothesis, zeta function, explicit formula, Jacobi operator, discrete spectral model, Selberg trace formula, GUE pair correlation, heat trace, Agmon wells, Kato-Rellich, zero-free regions, ψ(x) error bounds, Carlson theorem, Hardy spaces, Weyl law, holomorphic rigidity, CADC, arithmetic operator, spectral rigidity |
| url | https://doi.org/10.5281/zenodo.18664695 |