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 in {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, derived from the ether proper-time rate, 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 delta PMDL/delta Phi = 0 yields nabla^2 Phi = 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 (mod 7), establishing vacuum stability from first principles. The tau_c gravity mechanism yields exactly Newtonian gravity F = G_eff*M/(4*pi*b^2)*[1+O(sigma_AL/b)^2] in the continuum limit, derived analytically from the 3D Poisson Green's function. The quantum structure is derived: the tau_c clock is a valid Page-Wootters clock, deriving the Born rule P(k|tau) = ||^2 from the timeless universe state. Cross-tape gravitational coupling generates Bell nonlocality with CHSH parameter S = 2.4459 (86.5% of the Tsirelson bound), rigorously excluding all local hidden-variable models. Gravity and quantum entanglement are co-generated by the same 19-bit polynomial p(L,C,R)=C+R-CR-LCR over GF(7). All these structures emerge simultaneously via the Single-Source Principle. Key results are machine-certified in Lean 4 with zero sorry. Two falsifiable predictions with zero free parameters: r = 0 (no primordial gravitational waves) and delta_CP = 205.71 degrees.