Non-Equilibrium Stochastic Drift Amplification Coupled to Molecular AI Free-Energy Tensors and Post-Quantum Goldilocks Hardware Interlocks (PHOENIX_ROUTER)

Contemporary molecular artificial intelligence platforms—such as AlphaFold 3 and AlphaMissense—compute atomic-scale folding free-energy perturbations (ΔΔ G) and missense pathogenicity functionals under an implicit equilibrium panmictic (ideal-gas) population assumption. In physical reality, human populations inhabiting topographically partitioned archipelagos evolve as non-equilibrium statistical ensembles undergoing exponential demographic contraction. Building upon our prior treatises (10.5281/zenodo.23581227, 10.5281/zenodo.23581970, and 10.5281/zenodo.23589190), this monograph formalizes the mathematical and physical-layer computational core bridging microscopic molecular AI operators to macroscopic non-equilibrium Wright-Fisher diffusion and post-quantum cryptographic hardware governance. First, we establish the Non-Equilibrium Drift Amplification Theorem (Theorem 3.1), proving via continuous-time Fokker-Planck / Wright-Fisher diffusion that exponential contraction of local effective population size Ne,d(t) = Ne,d(0)e-γd t (γd > 0) drives an exponentially growing drift hazard hd(t) = eγd t/(2Ne,d(0)), ensuring strictly positive time-derivatives of autosomal recessive incidence (dIₗ(t)/dt > 0) even in the complete absence of consanguinity (FIS ≡ 0). Second, to prevent algorithmic rationing or age-based fiscal discontinuities ("Age-18 Subsidy Cliff") when deploying high-cost molecular therapies, we formalize the Post-Quantum Hardware Interlock Theorem (Theorem 5.1) over the 64-bit Goldilocks prime field (Fₚ, p = 2⁶⁴ - 2³² + 1). Using Poseidon2 Merkle commitments, FRI-based STARKs (Q-SAFA) with soundness error εsound < 2⁻¹²⁸, side-channel zeroization (RTO P2.0, Iₗₑₐₖ = 0), and an FPGA/ASIC pre-execution circuit breaker (PHOENIX_ROUTER, Δ t < 500 ns), any policy transition operator P_τ exhibiting a non-zero age-sensitivity Jacobian Ccliff(P_τ) ≡ 0 p physically grounds the ledger write-enable line prior to state mutation, mathematically enforcing Human-in-Command (HIC) and the Strict No-Learn Covenant (NLL-v1.0-2026).