Discrete Symplectic Cosmology: Non-autonomous Evolution on a Planck Lattice and an Effective Einstein Equation with Time-dependent Cosmological Term

We propose a theoretical framework — Discrete Symplectic Cosmology (DSC) — in which cosmic evolution is modeled as a non-autonomous discrete dynamical system on a Planck-scale lattice Z^3 x N, equipped with a symplectic structure. From two assumptions (discrete spacetime and symplectic evolution), we derive: (i) an adiabatic cooling law mu(n) = mu_c + (alpha_F/2)/ln^2(n) with the Feigenbaum constant alpha_F determining the cooling rate; (ii) an effective Einstein equation Gmu nu + Lambda(t) gmu nu = (8 pi G/c^4) Tmu nu where Lambda(t) = Lambda_infty + (4 d_H^2 / 3c^2) / (t^2 ln^2(t/t_P)) and d_H = ln2/ln(alpha_F) is the attractor Hausdorff dimension; and (iii) a Hubble relaxation law H(t) = H_infty + beta/ln^2(t/t_P) with beta < 0 derived (not fitted) from attractor contraction in the extended phase space. We illustrate the framework's observational consequences with mock-data comparisons for fine-structure drift, Hubble-parameter evolution, and laboratory clock constraints. Planck-epoch numerical simulations using a Stormer-Verlet integrator confirm the analytic cooling law over 60 decades of lattice time while preserving the symplectic form to machine precision. The framework makes falsifiable predictions, including an asymptotic Hubble limit H_infty testable by next-generation BAO surveys.