QMU Ledger Decomposition of the Hydrogen 2S–6P Transition: Proton Radius, Geometric Phase, and Aether Fine Structure

This work presents a Quantum Measurement Units (QMU) ledger-based decomposition of the hydrogen 2S--6P transition, using the Aether Physics Model (APM) as a geometric framework for interpreting atomic structure. The analysis is anchored to the 2026 high-precision spectroscopic measurement yielding a proton charge radius of rₚ = 0. 8406 (15) \, fm. The hydrogen spectrum is reformulated as a perturbative expansion in the fine-structure constant on a single base frequency scale Fq = mₑ c² / h. The conventional decomposition into Dirac, radiative (Lamb shift), and finite-size contributions is translated into QMU ledger form using the Compton wavelength C = h/ (mₑ c) and the invariant relation Fq C = c. A central result is the derivation of the proton finite-size frequency shift in QMU form: \ ₅₈₍₈ₓ₄ (2S) =-²3\, ⁴ (mᵣmₑ) ³ (rₚC) ²Fq, mᵣ is the reduced mass. This expression is obtained by direct substitution from the conventional bound-state QED formulation using = h/ (2) and C = h/ (mₑ c), preserving dimensional and scaling consistency. Inversion of this relation provides a direct extraction of the proton charge radius from the measured frequency shift, yielding agreement with experiment at the 10^-3\, fm level when recoil is included through the factor (mᵣ/mₑ) ³. Within the QMU framework, the finite-size correction is interpreted as a geometric traversal mismatch between the electron’s bound-state path and the proton’s distributed Aether structure. The proton radius emerges as a dimensionless geometric ratio rₚ/C, linking nuclear structure directly to the electron Compton scale without introducing additional fundamental lengths. The paper also establishes a ledger identity flow connecting the Aether unit closure relationᵤ curl = Fq² C² the observed hydrogen transition frequency, demonstrating that atomic structure can be expressed as successive geometric perturbations of a single invariant frequency scale. Predictions include stability of the ratio rₚ/C across hydrogenic systems, sensitivity of hyperfine structure to distributed charge anisotropy, and consistency between electronic and muonic hydrogen when reduced-mass effects are treated as a coupled inertial ledger. This work provides a geometrically unified interpretation of the proton radius within the QMU/APM framework and identifies experimental pathways for testing traversal-based effects in precision spectroscopy.