A Resonance-Driven Threshold Model for D-D Fusion via Irrational-Exponent Amplification

Cold fusion remains experimentally elusive due to the absence of a non-thermal mechanism capable of lowering the D–D Coulomb barrier. I propose a resonance-driven model arising from re-examining three idealizations in conventional physics: thermodynamic equilibrium, SI unit definitions, and the fixed value of c. These assumptions conceal digit-sensitive nonlinearities in structured lattices. I introduce a local energy expression E = m ⋅ f^{π/e}, where f is the Pd–D resonance frequency and π/e provides an irrational amplification exponent evaluated at high digit precision. Small perturbations of f, such as single-photon absorption, yield disproportionately large changes in tunneling probability. Numerical simulations show that 10⁶ absorbed photons at 780 nm raise the D–D tunneling probability to near certainty (an increase of 76.23 orders of magnitude), producing a sharp “resonance cliff.” This mechanism offers a falsifiable, non-thermal pathway for D–D fusion and may explain longstanding reproducibility challenges in LENR experiments. The formulation assumes the Observer is embedded within the physical system, not external to it. An experimentally falsifiable, mathematically explicit threshold formulation, constructed under realistic condensed-matter constraints, is included as Integrated Supplementary Information within this manuscript.