The Standard Model Fermion Spectrum as an Error-Correcting Code on a Holographic Surface

WITHDRAWAL / SUPERSESSION NOTICE (2026-05-31). Early kinematics paper subsumed by Part 01 (`The Holographic Circlette: Part 01 — The Encoding and Its Dynamics`). Current canonical version: doi.org/10.5281/zenodo.20478695. We propose a discrete computational framework in which stable data structures emerge as the valid codewords of an 8-bit quantum error-correcting ring code embedded within a 2D holo- graphic lattice.1 By applying four local Boolean constraints, we find that exactly 45 robust topo- logical states emerge from 256 possibilities. We identify a unique spectrum-preserving CNOT gate that serves as the deterministic update rule for this cellular automaton. From this purely information-theoretic foundation, we demonstrate remarkable structural isomorphisms to phys- ical phenomena: the continuum limit of the discrete quantum walk naturally reproduces the 3+1D Dirac equation, while the Fisher information metric of the error-correction syndrome distribution yields a Riemannian geometry mathematically identical to gravitational curvature. Furthermore, the topological invariants of this discrete network map cleanly to empirical phe- nomenological parameters of the Standard Model: the charged lepton mass ratios are derived to 0.007% precision from a geometric topological phase δ= 2/9, the weak mixing angle emerges as a structural bit-density sin2 θW = 2/9, and the W /Z boson mass ratio is recovered as a Ham- ming weight ratio 7/9. This framework suggests that the arbitrary continuous constants of physical field theories may be natively quantised properties of discrete quantum information routing.