Geometric Quantum Tunneling in the MMA–DMF Framework

We validate Geometric Quantum Tunneling (GQT) within the MMA–DMF framework, where barrier transmission is not imposed as a postulate but arises as a rare, noise-assisted escape process generated by deterministic scalar-field dynamics coupled to a structured vacuum sector. The stochastic forcing is thermodynamically constrained by a strict fluctuation–dissipation closure and regulated by a finite ultraviolet (UV) cutoff at a fundamental scale 𝑀 ≃ 1.00 × 102 TeV. Using a one-dimensional rectangular barrier as a controlled benchmark, we report: (i) Schrödinger-like wavepacket dispersion at Nelson equilibrium; (ii) recovery of semiclassical WKB scaling through an exponential dependence of transmission on barrier width (linear ln 𝑇 vs. width with 𝑅2 > 0.99 and a consolidated WKB recovery error of 1.2%); (iii) quantitative agreement with transfer-matrix quantum mechanics across deep-tunneling, resonant, and classical-transport regimes (RMSE 0.042, 0.085, and 0.011, respectively); and (iv) a distinctive near-cutoff prediction in which transmission is strongly suppressed as 𝑉0/𝑀 → 1 (rapid suppression already near 𝑉0 ≈ 0.95𝑀, with an inferred cutoff near 0.98𝑀 in the consolidated summary). Control tests include ablations that disable the geometric coupling, for which tunneling vanishes as expected. Numerical stability and convergence are verified with a step-size constraint 𝑑𝑡 ≲ 0.01𝑀−1; validated runs use 𝑑𝑡 = 0.005𝑀−1 with a small measured energy-drift slope (3.4 × 10−6) over 𝑇max = 1000. Data, scripts, and numerical artifacts required to reproduce the reported benchmarks are provided in the accompanying replication package.