Preprint · Release 16
Logarithmic Curvature Flow, Filament Localization, and the Geometric Origin of the Lepton Mass Spectrum
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 landing page provides accessible summaries and citation metadata for an archival preprint. The authoritative manuscript and downloadable files are maintained on the Zenodo DOI record. Wave Confinement Theory is an evolving independent framework; claims should be evaluated according to the derivations, simulations, experiments, data analyses, assumptions, and limitations stated in the paper itself.