Vibrational Lattice Theory: A Research Program

Vibrational Lattice Theory (VLT) proposes that all observed physicsemerges from a single vibrating 0-dimensional point obeying the simpleharmonic oscillator equation. Bidirectional propagation through threemutually orthogonal planes self-generates an infinite nested cubiclattice, governed by a universal 5% recycling constant derived from thecyclic closure geometry. The framework is structurally zero-free-parameter: every numerical quantity has a geometric origin in thelattice, with one physical scale (the electron mass) as the only input. This deposit contains the complete v1. 44 research program: a 14-pageshort paper submitted to Foundations of Physics, the full 119-pagelong-form paper with all derivations, the 43-page appendices, the gapsimulation companion (6 pages), the companion letter (7 pages), and twoPython source files implementing the gap and abundance simulations forreproducibility. Key results derived with no fitted parameters beyond the latticestructure: matter density of the universe at 4. 9% (Planck) ; SU (3) xSU (2) x U (1) gauge group with 12 generators; the fine structureconstant (0. 034% gap) ; Newton's constant (0. 355%) ; all charged leptonmasses; all six quark masses to under 1. 1% (closed in v1. 44 via thepast-Kₙ boundary attenuation factor) ; the Weinberg angle (-0. 37%) ;W, Z, and Higgs boson masses (under 1%) ; neutrino mass (0. 9%) ; theHubble tension (0. 17%) ; and the gravitational wave radiated fraction (5 +/- 1% predicted vs LIGO 4. 42 +/- 0. 80%). The framework states 58falsifiable predictions, 12 confirmed against independent publisheddata. Several derivations (notably the down-quark base factor, the Kₙ/Kₚplane ratio, and the bottom-quark face-diagonal weighting) remainidentified by their geometric content rather than derived from a singleintegral. These are explicitly flagged as open problems. Section 1. 1of the short paper defines precisely what "zero free parameters" meansin VLT. AI-assisted tools were used for mathematical verification, LaTeXformatting, and copy editing; all conceptual content, derivations, and final wording were developed and approved by the author.