Comprehensive Derivation Summary of the Fine-Structure Constant α ≈ 1/137 Based on 4D Honeycomb Lattice Topology

This paper constructs a complete theoretical framework based on the axiom system of four-dimensional honeycomb elastic primitive close-packing vacuum lattice. Two mutually independent first-principle derivation paths are proposed to resolve the fine-structure constant α=1/137 : the micro spherical extrusion dynamic deduction of electron 19-primitive clusters, and the dimensional reduction topological geometric derivation from 4D to 3D projection. All core characteristic constants including the limit retardation coefficient Kmax=150, pressure relief time ratio r_{total}=0.26, vibration critical amplitude threshold x0=0.68 and vacuum steady-state retardation coefficient Kvac=137 are uniquely analytical solutions solved from geometric integral and phase constraint equations, without artificially fitted parameters. Systematic numerical deviations of 0.67% and 0.8% originate from the natural projection reading difference between 4D curved lattice and 3D flat observation space, and a 0.9% fixed offset exists between the theoretical intrinsic benchmark light speed c0 and laboratory measured light speed caused by lattice secondary geometric corrections. Recurrence rules of kissing numbers for 2D–6D symmetric lattices and balloon-type projection scaling formulas are defined, and the volumetric topology and cross-sectional area topology double verification both converge to the intrinsic constant 137 of vacuum lattice. Three independent mathematical chains derive the unified pressure relief ratio 0.26, which verifies the self-consistency of the whole model. Furthermore, four falsifiable quantitative experimental predictions are put forward to test the rationality of the theoretical system. The applicable scale of this model is confined to the interval from Planck scale to subatomic scale. In addition, two preprint papers authored by Zenodo on lattice intrinsic light speed and dimensional gravitational topology provide cross-system geometric support for the fundamental axioms of the present model.