The GTE Polynomial as Unified Field Theory: One 19-Bit Description for Spatial Dynamics, Gauge Coupling, Gravity, Entanglement, and Baryon Number

A single polynomial p(L,C,R) = C + R - CR - LCR (mod 7), requiring 19 bits to specify, simultaneously generates five fundamental physical structures: spatial cellular-automaton dynamics achieving Rule 110 Turing universality (Class 4 complexity), conservation of Standard Model gauge vertices via Z_7 winding arithmetic, gravitational coupling via the Poisson equation nabla^2 Phi = G_eff * p(w_x, w_y, w_z), quantum entanglement with negativity N = 0.24, and Bell nonlocality with CHSH parameter S = 2.4459 (86.5% of the Tsirelson bound 2*sqrt(2)), with local hidden-variable models rigorously excluded. The additional specification cost for each role beyond the first is zero: K_extra = 0 in every case. The tau_c shared clock satisfies all Page-Wootters prerequisites, yielding a first-principles derivation of the Born rule. The 3D Poisson equation sourced by p(w_x,w_y,w_z) gives the exact Newtonian potential recovering F proportional to b^{-2} in the classical limit with computable corrections. From the same 19-bit description we derive: (i) color confinement as an MDL theorem with description-length gap delta K = log_2(9) ≈ 3.17 bits forbidding free colored quarks; (ii) the number of colors N_c = 3 from the three-tape architecture; (iii) baryon number B = (1/3)*sum chi_q(w_j) as a topological charge with B = 1/3 per quark; (iv) the SM fermion/boson split identified algebraically with the non-primitive roots of Z_7*; and (v) lepton-W universality as a consequence of shared Z_7 winding sectors. The Physical MDL variational principle yields gravitational attraction as local MDL minimization, while the global MDL residual — established from undecidability of the halting problem in the Perfect Self-Containment (PSC) framework — gives the cosmological constant. The zero-parameter prediction Omega_Lambda = (ln(2)/3*pi)*L_PSC = 0.6899 is within 0.70 sigma of the Planck 2018 value. The vacuum w = 0 is proved to be the unique fixed point of p(x,x,x) = x (mod 7). All foundational results are machine-certified in Lean 4 with zero sorry.