The Hydrogen Bond II: Ring-Down Harmonics of Coupled Geometric Oscillators

The Hydrogen Bond paper derived the hydrogen binding energy to 0.006 parts per trillion using a harmonic expansion with six coefficients, all expressed in terms of icosahedral geometry {V=12, E=30, F=20, χ=2, D=3}. This companion paper provides the physical interpretation: the coefficients are not fitting parameters but a dynamical narrative. When an electron (face mode, bridge 108) meets a proton (vertex mode, bridge 11×3), they couple through injection locking and the merged system rings down through successive harmonics to ground state. Each coefficient maps to a specific physical event in the binding process: approach, self-recognition, proton pushback, injection locking, and post-merger settlement. The α⁵ term at the quintic barrier (Abel–Ruffini theorem) marks the transition from dynamic coupling to structural settling. The final two terms (α⁶, α⁷) are the ring-down of the merged system. The topology twins c₃ = +χ/(F+χ) and c₇ = −χ/(V+χ) confirm that proton and electron are opposite ends of the same geometric twist, settling simultaneously through the Euler characteristic.