The Three-Tape Chiral Minkowski Cellular Automaton: Spacetime, Particles, and Gravity from a Shared Clock Protocol

We introduce the three-tape Chiral Minkowski Cellular Automaton (CMCA): three independent one-dimensional CMCAs — each composed of chiral Rule 110 and Rule 124 outer layers gated by an inner tau_c clock — sharing a single outer clock period tau_c_out. We prove the Dimensional Protocol Principle (DPP): this shared clock is both necessary and sufficient for 3+1D dynamics. Without it, the three tapes evolve as independent 1+1D systems; with it, they exhibit a single 3+1D spacetime. Under the DPP construction, uniform winding triples (w,w,w) for w 0,2,3,4,6 recover the full Standard Model particle spectrum via Z_7 winding conservation, with all 33 Standard Model charged-current vertices verified. Color confinement, baryon number as a topological charge, and the three-tape holographic information scaling (3L/L^3 0, realizing Bekenstein–Hawking area scaling) are additionally machine-certified in Lean 4. The clock ratio tau_c_ratio = 3/7 0.4286 < 1, derived from the ether proper-time rate (EtherProperTimeRate.lean, ), provides a built-in time-dilation mechanism. Rule 110 carries right-chirality and Rule 124 carries left-chirality, realizing the V-A structure of the weak interaction at the cellular-automaton level. Gravitational attraction arises from cross-tape PMDL minimization. The variational equation / = 0 yields ^2 = G eff p, where p is the GTE polynomial. The vacuum w=0 is proved to be the unique fixed point of p(x,x,x) x 7, establishing vacuum stability from first principles. The _c gravity mechanism yields exactly Newtonian gravity F = G effM/(4 b^2)[1 + O( AL/b)^2] in the continuum limit b AL, derived analytically from the 3D Poisson Green's function (CatAD). The three formulations of the mechanism — gradient kick, linearized GR metric, and the equivalence principle — are equivalent in the Newtonian limit. The quantum structure is derived: the _c clock is a valid Page–Wootters clock (CatAD), deriving the Born rule P(k|) = | k|U()|_0|^2 from the timeless universe state. Cross-tape gravitational coupling generates Bell nonlocality with exact CHSH parameter S = 2.4459 (86.5 rigorously excluding all local hidden-variable models. Gravity and quantum entanglement are co-generated by the same 19-bit polynomial. Permanent solitons arise via ether-period-14 resonance. All of these structures — spacetime, matter, gravity, and quantum mechanics — emerge from a single 19-bit polynomial p(L,C,R)=C+R-CR-LCR over GF(7) in five physical roles simultaneously (Single-Source Principle), a structural consequence of MDL minimality selecting the unique polynomial consistent with all PSC constraints. Key results are machine-certified in Lean 4 with zero sorry. We derive two falsifiable predictions with zero free parameters: r = 0 (no primordial gravitational waves) and _CP = 205.71^.