Spectral and Geometric Projections of Invariance: The Recursion Constant Across Nature
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2025
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| _version_ | 1866901800409366528 |
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| author | Julian, Joseph |
| author_facet | Julian, Joseph |
| contents | <p>This paper explores the hypothesis that the dimensionless mass ratios of the Standard Model and the dimensional constants of nature—such as $\hbar$, $c$, and $G$—represent dual projections of a single invariant parameter of recursion geometry. Within the general framework of CPT–Coherence (Mirror–Mind) Theory, physical systems are described by fields $\Psi(x^\mu,\tau)$ possessing an additional coordinate $\tau$ corresponding to coherence depth. A universal, dimensionless quantity $\Delta\hat{\tau}_R$, the \emph{recursion constant}, governs spacing between stable $\tau$-eigenmodes. When projected spectrally, this invariant manifests as the logarithmic pattern of particle masses; when projected geometrically, it manifests as the fixed ratios among the fundamental constants. The analysis presented here remains entirely theoretical and non-proprietary, addressing only invariant structure rather than algorithmic or computational realization.</p> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_17479667 |
| institution | Zenodo |
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| publishDate | 2025 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Spectral and Geometric Projections of Invariance: The Recursion Constant Across Nature Julian, Joseph spectral invariance geometric projections mass hierarchy invariants standard model mass ratios recursion symmetry $\tau$-recursion geometry $\tau$-covariant dynamics $\tau$-Lorentz invariance eigenmode structure recursion potential Mirror-Mind Theory CPT-Coherence recursive geometry $\tau$-curvature operator awareness kernel recursive collapse operator operator algebra of coherence $\tau$-action functional recursion constant coherence manifold TauSolver Prism spectral decomposition eigenvalue projections recursion eigenbasis Hamiltonian assembly log-spectral mapping spectral flow invariance geometric eigenmodes boundary condidtion analysis recursive solver stability unified mass geometry recursion-induced symmetry self-similar field hierarchy scale-free dynamics mass-energy correspondence recursive unification framework topological coherence information geometry of mass spectral topology $\tau$-manifold curvature <p>This paper explores the hypothesis that the dimensionless mass ratios of the Standard Model and the dimensional constants of nature—such as $\hbar$, $c$, and $G$—represent dual projections of a single invariant parameter of recursion geometry. Within the general framework of CPT–Coherence (Mirror–Mind) Theory, physical systems are described by fields $\Psi(x^\mu,\tau)$ possessing an additional coordinate $\tau$ corresponding to coherence depth. A universal, dimensionless quantity $\Delta\hat{\tau}_R$, the \emph{recursion constant}, governs spacing between stable $\tau$-eigenmodes. When projected spectrally, this invariant manifests as the logarithmic pattern of particle masses; when projected geometrically, it manifests as the fixed ratios among the fundamental constants. The analysis presented here remains entirely theoretical and non-proprietary, addressing only invariant structure rather than algorithmic or computational realization.</p> |
| title | Spectral and Geometric Projections of Invariance: The Recursion Constant Across Nature |
| topic | spectral invariance geometric projections mass hierarchy invariants standard model mass ratios recursion symmetry $\tau$-recursion geometry $\tau$-covariant dynamics $\tau$-Lorentz invariance eigenmode structure recursion potential Mirror-Mind Theory CPT-Coherence recursive geometry $\tau$-curvature operator awareness kernel recursive collapse operator operator algebra of coherence $\tau$-action functional recursion constant coherence manifold TauSolver Prism spectral decomposition eigenvalue projections recursion eigenbasis Hamiltonian assembly log-spectral mapping spectral flow invariance geometric eigenmodes boundary condidtion analysis recursive solver stability unified mass geometry recursion-induced symmetry self-similar field hierarchy scale-free dynamics mass-energy correspondence recursive unification framework topological coherence information geometry of mass spectral topology $\tau$-manifold curvature |
| url | https://doi.org/10.5281/zenodo.17479667 |