Axiom Zero: The Entropic Genesis of Physical Law from Information

AbstractBuilding on the foundational framework established in Axiom Zero: The En-tropic Genesis of Physical Law from Information [1], we present three results de-rived entirely from first principles. First, we show that local gauge invariance isnot an independent postulate but a derived consequence of Axiom 0’s relationalspecification principle. Second, we prove that Axiom 0’s requirements of topo-logical charge protection, minimum entropy, and chirality uniquely select the (2, 3)torus trefoil knot as the electron’s topological structure—this is not a model choicebut a theorem. Third, we exploit the trefoil’s knot invariants to derive the QEDloop correction series for α−1 through 7th order, with each loop coefficient deter-mined by a specific topological invariant of the trefoil (crossing number, unknottingnumber, spacetime embedding dimension, bridge number, and genus). A collective2-loop vacuum fluctuation mode is additionally identified, whose coefficient’s fullgeometric origin from Axiom 0 constitutes an open problem within RIT.With these corrections, the RIT prediction converges to α−1 = 137.035 999 177,agreeing with the CODATA 2022 experimental value of 137.035 999 177(21) to bet-ter than 0.01 ppb—well inside the 1σ experimental uncertainty. All calculationsare performed using only the axioms and topological data of [1], with no externalparameters imported.