Geometric Resonance and Binary Partition in Proton Structure: An Analytical Derivation of the Charge Radius

The "Proton Radius Puzzle" has highlighted significant discrepancies between electron scattering measurements and recent muonic hydrogen spectroscopy. This paper proposes a phenomenological approach based on geometric resonance to derive the proton charge radius from first principles.

We postulate that stable baryonic structure emerges from an orthogonal decomposition of the Compton frequency, governed by a sequential binary bifurcation condition (n=2). Without introducing free parameters, this framework analytically derives a charge radius of 0.8412 fm. This value shows a 99.98% agreement with the 2018 CODATA recommended value (0.8414 fm). Furthermore, we identify a dimensionless structural constant κ ≃ 4, suggesting that the proton size is fixed by a fundamental relativistic confinement scale rather than arbitrary parameter fitting.