Geometric Quantum Tunneling in the MMA–DMF Framework

We present a technical validation of Geometric Quantum Tunneling (GQT) within the MMA-DMF framework. In this approach, barrier penetration is not postulated: it emerges as a deterministic, noise-assisted escape process generated by a scalar-field generalized Langevin dynamics whose stochastic sector is thermodynamically closed by a strict fluctuation--dissipation relation [1, 2] and regulated by a finite ultraviolet (UV) cutoff at a fundamental scale M≃1.00×102 TeVM \simeq 1.00 \times 10^{2}\,\mathrm{TeV}M≃1.00×102TeV. We report 1D benchmark results showing (i) Schrödinger-like dispersion calibration at Nelson equilibrium, (ii) WKB recovery via exponential transmission scaling with barrier width (linear ln⁡T\ln TlnT vs width with R2>0.99R^{2} > 0.99R2>0.99 and a consolidated WKB recovery error of 1.2%), (iii) quantitative isomorphism against transfer-matrix quantum mechanics across energy regimes (deep-tunneling RMSE 0.042, resonant RMSE 0.085, classical-transport RMSE 0.011), and (iv) the distinctive “geometric wall” prediction that tunneling collapses as V0/M→1V_{0}/M \to 1V0/M→1 (rapid suppression already near V0≈0.95MV_{0} \approx 0.95MV0≈0.95M and an inferred cutoff near 0.98M0.98M0.98M in the consolidated summary). We include mandatory ablations via the geometric toggle αgeo\alpha_{\mathrm{geo}}αgeo (tunneling vanishes as αgeo→0\alpha_{\mathrm{geo}} \to 0αgeo→0), and stability/convergence constraints requiring Δt≲0.01 M−1\Delta t \lesssim 0.01\,M^{-1}Δt≲0.01M−1 with validated production operation at Δt=0.005 M−1\Delta t = 0.005\,M^{-1}Δt=0.005M−1 and an energy drift slope 3.4×10−63.4 \times 10^{-6}3.4×10−6 over tmax⁡=1000t_{\max}=1000tmax=1000. Finally, we specify a reproducibility and integrity layer (bit-exact seed replay across hardware targets, deterministic checkpointing, and SHA-256 manifesting) intended to make the full pipeline externally auditable. The consolidated evidence supports that MMA-DMF reproduces standard low-energy tunneling phenomenology while making a falsifiable high-energy prediction tied to UV regulation.