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: gravity as the curvature of the Fisher information metric; special relativity as a bandwidth constraint on the computational substrate; the cosmological constant as the vacuum information floor; and a resolution of the black hole information paradox via computational phase transition at the horizon. We demonstrate that the vacuum Fisher information $\mathcal{F}_{\text{vac}}(a)$ is not static but evolves due to competing effects of constraint establishment and matter dilution, yielding a dynamic dark energy model $\mathcal{F}_{\text{vac}}(a) \propto a^{\alpha} \exp(-\beta\, a^{\gamma})$ that matches DESI DR2 observations to within 1.5\%. The mass hierarchy is explained through lattice criticality, with the Koide relation for charged lepton masses emerging from the $\mathbb{Z}_3$ symmetry of the generation sector. The framework reinterprets pair production (the Schwinger effect) as dielectric breakdown of the error-correcting code, and predicts exactly three sterile neutrinos as pseudocodewords of the lattice. We further show that the continuous wave equations of quantum mechanics are not fundamental but emergent. The 1+1D Dirac equation is derived exactly as the continuum limit of a discrete quantum walk whose coin operator is the CNOT gate. The Dirac mass term $mc^2\sigma_x$ is literally the Pauli-X operator - the Boolean NOT gate acting on the isospin bit $I_3$. Rest mass is the CNOT execution frequency. The complex structure of quantum mechanics (the imaginary unit $i$) is forced by the unitarity requirement of a reversible Boolean swap. The Schr"odinger equation follows as the non-relativistic limit. Leptons ($LQ=0$), which bypass the CNOT entirely, propagate as massless Weyl fermions at $c$ in the bare theory. The lattice does not obey quantum mechanics. Quantum mechanics obeys the lattice.