The Mass-Energy-Information Equivalence: A bottom-up identification of the particle spectrum via FCC lattice error correction

Does information possess physical mass? Modelling the physical vacuum as a substrate-free quantum error-correcting code suggests that an elementary particle’s mass is simply its fault-tolerant verification cost. We test this Mass-Energy-Information (M/E/I) equivalence on the Face-Centred Cubic (FCC) lattice, tracking defects within a [ 192 , 130 , 3 ] CSS code. Through a bottom-up classification of all possible defect geometries, we filter 25 candidate states through four strict thermodynamic and topological axioms — Minimum Topological Dimension, Sector Completeness, Boundary Closure, and Kinematic Shedding — each derived from established QEC theory or lattice gauge theory. Exactly 5 physically stable states survive this sieve. Their verification costs — 1, 207, 273, 1836, and 1839 — match the empirical mass ratios of the electron, muon, pion, proton, and neutron to within 0.12%. The rejected configurations violate specific physical constraints and match no known particles. No parameters are fitted. This offers highly constrained macroscopic evidence that inertial rest mass is the thermodynamic shadow of quantum error correction overhead.