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 ( ): three one-dimensional sharing a single outer clock period τcout, each with chiral Rule~110 and Rule~124 layers gated by an inner τc clock. We prove the Dimensional Protocol Principle (DPP): this shared clock is necessary and sufficient for 3+1D dynamics. Without it the tapes evolve as independent 1+1D systems; with it they realize a single 3+1D spacetime. Under the DPP construction, uniform winding triples recover the full Standard Model particle spectrum via winding conservation, with all 33 charged-current vertices verified. Color confinement, baryon number as a topological charge, and three-tape holographic information scaling (realizing Bekenstein–Hawking area scaling) are machine-certified in Lean~4 with zero . The clock ratio τcratio = 3/7 ≈ 0.4286 provides a built-in time-dilation mechanism, analytically derived from the ether proper-time rate. Rule~110 carries right-chirality and Rule~124 left-chirality, realizing the V-A structure of the weak interaction. Gravitational attraction arises from cross-tape PMDL minimization. The variational equation δ /δΦ = 0 yields Newtonian gravity in the continuum limit, derived analytically from the 3D Poisson Green's function. The vacuum is Ricci-flat and the Gorard normalization constant C_ Gorard = 3/32 is exact; both are machine-certified in Lean~4 with zero . The τ_c clock is a valid Page–Wootters clock, deriving the Born rule from the timeless universe state. Cross-tape gravitational coupling generates Bell nonlocality with exact 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. All structures — spacetime, matter, gravity, and quantum mechanics — emerge simultaneously from the single 19-bit polynomial p(L,C,R)=C+R-CR-LCR over (7) (Single-Source Principle, a consequence of MDL minimality). Falsifiable predictions: r=0 and δ_CP = 205.71^ .