Four Fundamental Constants of Nature from a Gated Cubic Recursion with Zero Free Parameters

First paper of the RASP series. Derives four fundamental constants of nature — proton-to-electron mass ratio, neutron-to-electron mass ratio, inverse fine-structure constant, and muon-to-electron mass ratio — from a single gated cubic recursion f(x) = Γ·tanh³(x) − λx with zero free parameters. All constants emerge from the integers (n,p) = (3,5) through Diophantine, modular arithmetic, and spectral constraints. Includes 106 computational verification scripts. Research began June 2025.