Vibrational Field Dynamics (VFD)
A Structural Approach to Particle Mass from Spectral Geometry
Most fundamental constants in physics are measured, not derived. We present a geometric expression for the proton–electron mass ratio:
Observed: 1836.15 · No fitted continuous parameters
Founded by Lee Smart
This work explores whether particle mass ratios can be recovered from geometric and spectral structure alone. The framework is a constrained model, not a full theory. It uses a small number of explicit assumptions and produces a compact expression for the proton–electron mass ratio. Supporting papers develop the structure, limits, and extensions of this result.
Paper Hierarchy
The standalone entry point. Recovers mp/me = φ1265/81 ≈ 1835.8 from closure geometry with zero fitted continuous parameters. Includes 12-objection adversarial review and sensitivity analysis. Externally readable without prior VFD context.
Exact eigenvalue correspondence (λ = 15 = ΔC). Includes retraction of earlier spectral dimension claim.
No-go theorem for shell-extension leptons. Conditional winding operator (muon 0.5%, tau 3.7%).
Development paper. Documents the combinatorial invariant and three-order mass law that Paper IV formalises.
Exploratory extension of the mass programme with high-accuracy numerical correspondences across 13 particles. Not the primary entry point.
All derivations, scripts, and verification tools are available for independent inspection at github.com/vfd-org/vfd-crystallisation. The repository includes LaTeX sources, Python simulation code, and reproducibility guides for all results.
Ongoing & Related Work
The mass programme sits within a broader research framework. The following areas are ongoing investigations — earlier-stage and more speculative than the primary mass result.
Engineering programmes informed by VFD's structural ideas. These are applied directions, not proof of the underlying framework.
Follow the Work
Open research programme. New papers and analysis published in real time.