Lattice Mechanics, Geometry of Matter

This article reanalyzes the foundations of particle physics from experimental and observational facts, through a methodology that rethinks the hierarchy of evidence and places observational invariants above formalism. The analysis converges on a single structure: space at the particle scale is a three-dimensional cubic lattice, of which particles, photons, and all physical phenomena are deformations transmitted as discrete waves. Charge duality arises from the vacancy/excess duality of lattice nodes and is identified as the real matter/antimatter symmetry; mass arises from the geometric configuration of the lattice around the charge. A new fundamental quantity ξ = mec2 = 0.511 MeV sets the energy scale of the lattice, whose spacing is the reduced Compton wavelength ƛC. The three-dimensional structure of the proton is identified, yielding a purely geometric derivation of the fine-structure constant, 1/α = 82 + 82 + 32 × (1 + ζ3) = 137.036121592 with ζ = √3/2 − 1/√2, and of the proton mass, mproton = 3 × (1/α + 1 + ζ2 × 1372) × ξ = 938.272087 MeV. Charge alternation emerges as the single mechanism behind atomic, molecular, and nuclear binding: the electron loses its orbitals, the neutron reverts to a proton–electron pair, the deuteron becomes a p+e−e+e−p+ chain, and nucleosynthesis is reread as sequences of exothermic reactions. Relativity is reread within a latticed frame clocked at c, and the Higgs mechanism is rejected. This work has been submitted for peer review.