Quantum Mechanics from Rule 110: Hilbert Space, Hamiltonian, and Born Rule

We apply 't Hooft's cellular automaton interpretation of quantum mechanics to the GTE cellular automaton fMDL on Z₇⁵, the 16, 807-state visible-sector ring encoding the Standard Model generation structure. The complete orbit decomposition of fMDL () reveals a single cycle: the vacuum fixed point (0, 0, 0, 0, 0) with E=0. The physical Hilbert space is one-dimensional; fMDL belongs to 't Hooft's information-loss regime. SM generation states are transients with tail lengths (gen₁) =3 > (gen₂) =2 > (gen₃) =1, matching the empirical stability hierarchy (). A direct eigenvalue-to-mass correspondence is falsified on every formulation tested (). The Two-Role Structural Principle () separates roles: the cogwheel construction provides Hilbert space structure, unitarity, and the Born rule (, Lean-certified) ; the GTE Nₑff cascade provides the mass spectrum. The seven winding-equivalence classes of Z₇⁵ (, gauge\ₐrithmetic\ᵢdentification) are identified as 't Hooft's information-equivalence gauge classes (): the five SM winding sectors \0, 2, 3, 4, 6\ yield U (1) EM, SU (2) L, and SU (3) c; sector W=1 predicts the SU (5) Y-leptoquark; the X-leptoquark (Q=+4/3) cohabits W=4. The AFCA causal graph is update-schedule-independent (Lean-certified) ; discrete Minkowski causal cones are embedded with coordinate surjection certified. Full Minkowski bijection remains open ().