The Universal Geometric Matrix of Matter

ABSTRACT This paper presents a novel, comprehensive geometric matrix of fundamental matter (including leptons, baryons, and multi-nucleon atomic clusters) derived within a unified framework of an elastic vacuum network. We demonstrate that the fundamental parameters of the electron and the proton, traditionally viewed by conventional academic physics as isolated, empirical constants, are strictly cross-locked through a single underlying structural software operating within the spatial fabric.By introducing the concept of the dimensionless network macro-lever, we prove that the generational shift between the electron (lever: 253.2754) and the proton (lever: 0.137937) is governed by a strict, whole-number scaling ratio of the spatial gearbox matching the mass-coordination matrix. For the proton node, we present three independent theoretical channels to derive its structural parameters, revealing a multi-stage linear boundary cascade that steps outward from the core Schwarzschild preform, through the internal Compton mass vortex, to the official 0.8414 fm electromagnetic charge shell via a clean geometric scaling factor of 4.Furthermore, we extend this structural software to macroscopic atomic systems, demonstrating that the nuclei of chemical elements (such as Helium-4 and Lithium-7) are not chaotic aggregates of loose nucleons bound by residual forces, but highly stable, geometric resonant bubbles stamped directly by the network's frame tension. The model provides direct kinematic derivations for extreme subatomic properties, including the 10^32 m/s² centripetal core acceleration, the 9088-Ampere internal circuit currents, and the 10^33 Pascal internal core pressures recently mapped by modern high-energy electron scattering experiments.Finally, the absolute mathematical consistency and closure of the proposed model is sealed across all material entities. We prove that the universal Planck length is the exact geometric mean between any particle's or cluster's cyclic wave vortex and its sub-quantum Schwarzschild preform divided by the network balance equator of 2. All calculations achieve absolute precision down to the last digit on a standard calculator, offering a rigorous, unified geometric alternative to conventional quantum field representations.