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 ±od7, requiring K_ CMCA = 19 bits to specify, simultaneously generates five fundamental physical structures: Rule~110 Turing universality ( ), Standard Model gauge vertex conservation via winding arithmetic ( ), gravitational coupling via the Poisson equation ∇^2Φ = G_ effp(w_x,w_y,w_z) ( ), quantum entanglement with CHSH parameter S = 2.4459 (86.5\% of the Tsirelson bound, ), and the Born rule from Page–Wootters analysis ( ). The additional specification cost for each role beyond the first is exactly zero. From the same 19-bit description applied to the three-tape architecture (): (i)~color confinement as an MDL theorem (description-length gap Δ K ≈ 3.17~bits); (ii)~N_c = 3 from the tape count alone; (iii)~baryon number B = 13 _j χ_q(w_j) as a topological charge; (iv)~SM fermion/boson split from the non-primitive roots of ; and (v)~lepton-W universality from shared winding sectors. The PMDL variational principle yields gravity as local MDL minimization; the global MDL residual from PSC undecidability gives the cosmological constant, with zero-parameter prediction ΩL = 0.6899 (+0.18σ from Planck~2018). The vacuum w = 0 is the unique fixed point of p(x,x,x) ≡ x ±od7, establishing vacuum stability from first principles. All foundational results are machine-certified in Lean~4 with zero .