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 f_ MDL on Z_7^5, the 16,807-state visible-sector ring encoding the Standard Model generation structure. The complete orbit decomposition of f_ MDL ( ) reveals a single cycle: the vacuum fixed point (0,0,0,0,0) with E=0. The physical Hilbert space is one-dimensional; f_ MDL belongs to 't~Hooft's information-loss regime. SM generation states are transients with tail lengths ( gen_1)=3 > ( gen_2)=2 > ( gen_3)=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 N_ eff cascade provides the mass spectrum. The seven winding-equivalence classes of Z_7^5 ( , \_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 ( ).