The Holographic Circlette: Unifying the Standard Model, Gravity, and Cosmology via Error-Correcting Codes on a Fisher-Information Lattice

We propose a unified physical framework in which the Standard Model fermion spectrum corresponds to the set of valid codewords of an 8-bit quantum error- correcting code defined on a holographic lattice. Four local constraints select exactly 45 valid matter states from 256 possibilities. The dynamics are governed by a unique update rule - a CNOT gate at the bridge-isospin boundary - identified as the weak interaction. From this information-theoretic foundation, we derive: the charged lepton mass ratios to 0.007% precision from a single geometric parameter δ= 2/9; the weak mix- ing angle sin2 θW = 2/9 (0.5% error); the W/Z boson mass ratio MW/MZ = 7/9 (0.06% error); and the PMNS neutrino mixing angles under a bimaximal lattice ansatz. Gravity emerges as the curvature of the Fisher information metric; special relativity as a bandwidth constraint; and the cosmological constant as the vacuum information floor. A dynamic dark energy model matches DESI DR2 observations to within 1.5%. The 3+1D Dirac equation is derived exactly as the continuum limit of a discrete quantum walk whose coin operator is the CNOT gate. Rest mass is the CNOT execution frequency. The complex unit i is forced by the unitarity of a reversible Boolean swap. The central result of this paper is that the integer ratio δ = 2/9 - the ratio of a 2-bit topological defect to a 9-bit plaquette - determines the charged lepton mass spectrum, the electroweak mixing angle, the Cabibbo angle, and the PMNS mixing matrix, with one continuous free parameter (the overall mass scale).