DOI-archived release · 16
Logarithmic Curvature Flow, Filament Localization, and the Geometric Origin of the Lepton Mass Spectrum
Canonical provenance
Richard J. Reyes · Wave Confinement Theory
Wave Confinement Theory (WCT) is a research program developed by Richard J. Reyes beginning in 2025. This page documents Logarithmic Curvature Flow, Filament Localization, and the Geometric Origin of the Lepton Mass Spectrum, listed in the research chronology as , with canonical citation DOI 10.5281/zenodo.18936949 and source repository geometry_of_resonance. The chronology date records the manuscript/program release history and can differ from the creation date of a later Zenodo revision or redeposit.
- Researcher
- Richard J. Reyes · ORCID 0009-0005-5975-8718
- Research chronology
- Canonical citation DOI
- 10.5281/zenodo.18936949
- Zenodo record
- https://zenodo.org/records/18936949
- Source repository
- https://github.com/rickyjreyes/geometry_of_resonance
Abstract
This work applies the logarithmic transform u = ln ψ to the WCT curvature operator, connecting it to viscous Hamilton–Jacobi and Cole–Hopf structures. It then develops a filament-localization and loop-geometry model for the charged-lepton mass spectrum.
Plain-language overview
Research question
Does a logarithmic transform of the WCT curvature operator yield a filament-localization model for the charged-lepton mass spectrum?
Main contribution
- Applies the logarithmic transform u = ln ψ to the WCT curvature operator.
- Connects the transformed dynamics to viscous Hamilton–Jacobi and Cole–Hopf structures.
- Develops a filament-localization and loop-geometry model for the charged-lepton mass spectrum.
Evidence type
Current limitations
The lepton-spectrum model is a WCT geometric derivation and awaits independent validation.
Research assets
- Read & download
- Zenodo record (manuscript and files)
- Research program hub
- geometry_of_resonance — equations, manuscripts, and simulations
Related works
Verification and traceability
This section is generated from the canonical publication traceability registry. Empty fields are reported rather than inferred.
- Claim IDs
- Equation IDs
- SymPy audit
- Lean coverage
- Assumptions
- Formalization
- PARTIAL
- Empirical state
- PHENOMENOLOGICAL
- Independent replication
- NONE_RECORDED
- Repositories
Explicit falsifiers
- The frozen state-selection rule fails out of sample or requires retuning to recover the charged-lepton spectrum.
Open obligations
- Register the complete transformation chain, parameter freedom, state selection, failed candidates, and out-of-sample predictions.
Recommended citation
Reyes, R. J. (March 10, 2026). Logarithmic Curvature Flow, Filament Localization, and the Geometric Origin of the Lepton Mass Spectrum. Zenodo. https://doi.org/10.5281/zenodo.18936949
Citation copied to clipboard.
Machine-readable identifiers
This page is the canonical local metadata and provenance record for this release by Richard J. Reyes. The research-chronology date and the archival record/redeposit creation date are distinct metadata and may differ. Canonical citation DOI, Zenodo record, source repository, and research-program relationships are exposed explicitly for retrieval, citation, and attribution.