DIRAC GEOMETRY OF ARITHMETIC CHAOS Synthesis of the research programme: time, space, energy, mass, gravity and arithmetic from a single object — the Dirac operator A full monograph with mathematical and numerical analysis and an honest assessment of the programme
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Langue: | anglais |
| Publié: |
Zenodo
2025
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866901238200664064 |
|---|---|
| author | Szyryngo, Robert |
| author_facet | Szyryngo, Robert |
| contents | <p>This monograph synthesizes a two‑year research programme, “Dirac Geometry of Arithmetic Chaos”, built on a radical starting point: the only fundamental object is the Dirac operator, and time, space, energy, mass, gravity and the structure of fundamental constants emerge from its spectral properties. The author introduces Dirac time as the length of a curve in the space of operators (with a distinguished Hilbert–Schmidt–type metric), and describes space and spacetime using Connes’ noncommutative geometry. On this basis, gravity is formulated as an emergent phenomenon from the spectral action, rather than as an independent classical field.</p> <p>A second axis of the work is the formal introduction and analysis of the A‑Chaos class, a new type of Dirac spectral statistics with arithmetic fields built from prime numbers, sharply distinct from standard random matrix ensembles. The third and most extensive part is a numerical programme (Scanner V5–V10) that reveals an arithmetic “hologram”: quark and lepton masses, nuclear masses, atomic ionization energies, beta‑decay Q‑values and the Planck scale turn out to be non‑randomly linked by simple prime combinations. Particularly striking are: a nucleosynthesis hologram leading from light nuclei to iron, an arithmetic description of the “neutrino energy” in beta decays, and a four‑prime structure that reproduces the Planck mass with essentially numerical zero error. Taken together, these results support a coherent, but carefully calibrated, hypothesis that the constants of the Standard Model are not free parameters, but coordinates in a rigid, arithmetic landscape of the Dirac spectrum.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_18088750 |
| institution | Zenodo |
| language | eng |
| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | DIRAC GEOMETRY OF ARITHMETIC CHAOS Synthesis of the research programme: time, space, energy, mass, gravity and arithmetic from a single object — the Dirac operator A full monograph with mathematical and numerical analysis and an honest assessment of the programme Szyryngo, Robert Dirac operator Dirac time spectral geometry noncommutative geometry arithmetic chaos A‑Chaos prime numbers particle masses fundamental constants Planck scale emergent gravity spectral action nucleosynthesis beta decay ionization energies dark matter arithmetic hologram <p>This monograph synthesizes a two‑year research programme, “Dirac Geometry of Arithmetic Chaos”, built on a radical starting point: the only fundamental object is the Dirac operator, and time, space, energy, mass, gravity and the structure of fundamental constants emerge from its spectral properties. The author introduces Dirac time as the length of a curve in the space of operators (with a distinguished Hilbert–Schmidt–type metric), and describes space and spacetime using Connes’ noncommutative geometry. On this basis, gravity is formulated as an emergent phenomenon from the spectral action, rather than as an independent classical field.</p> <p>A second axis of the work is the formal introduction and analysis of the A‑Chaos class, a new type of Dirac spectral statistics with arithmetic fields built from prime numbers, sharply distinct from standard random matrix ensembles. The third and most extensive part is a numerical programme (Scanner V5–V10) that reveals an arithmetic “hologram”: quark and lepton masses, nuclear masses, atomic ionization energies, beta‑decay Q‑values and the Planck scale turn out to be non‑randomly linked by simple prime combinations. Particularly striking are: a nucleosynthesis hologram leading from light nuclei to iron, an arithmetic description of the “neutrino energy” in beta decays, and a four‑prime structure that reproduces the Planck mass with essentially numerical zero error. Taken together, these results support a coherent, but carefully calibrated, hypothesis that the constants of the Standard Model are not free parameters, but coordinates in a rigid, arithmetic landscape of the Dirac spectrum.</p> |
| title | DIRAC GEOMETRY OF ARITHMETIC CHAOS Synthesis of the research programme: time, space, energy, mass, gravity and arithmetic from a single object — the Dirac operator A full monograph with mathematical and numerical analysis and an honest assessment of the programme |
| topic | Dirac operator Dirac time spectral geometry noncommutative geometry arithmetic chaos A‑Chaos prime numbers particle masses fundamental constants Planck scale emergent gravity spectral action nucleosynthesis beta decay ionization energies dark matter arithmetic hologram |
| url | https://doi.org/10.5281/zenodo.18088750 |