Topological Invariance and Nodal Phase-Lock: A Discrete Foundation for Leptonic Phases and Hadronic Slopes

This paper presents a formal audit of the CERN TOTEM elastic scattering data, identifying a high-precision match between the observed nuclear slope (B) and the PNI framework. We demonstrate that the slope of 19.96 +/- 0.04 GeV^-2 is not a phenomenological variable, but a direct derivation from a 7,200-state discrete lattice (K) and its fundamental refractive index (n_Upsilon ≈ 1.0822). Key Contributions: Empirical Verification: Direct first-principles derivation of the 19.958 GeV^-2 slope, matching LHC measurements at sqrt(s) = 8 and 13 TeV. Barkhausen Jitter Prediction: A specific call for Fourier analysis of dσ/dt residuals to detect the 1.0822 lattice harmonic—the "hum" of a quantized vacuum. Gravitational Extension: Application of the Nodal Saturation Limit to predict a -0.116 phase-inverted reflection coefficient for gravitational wave echoes, providing a macroscopic test for the framework. Unification: Connects the hadronic "elasticity" of the proton to the "reflectivity" of saturated informational boundaries (Black Holes) through a singular, topological constant.