ICCXXIII:TheHydrogenAtomfromStochastic CopyingDynamics

We derive the hydrogen atom’s bound state within the Information‑Copying Cosmology (ICC) framework. Building on emergent gauge fields (ICCX) and fermionic defects (ICCXI), we demonstrate that the Coulomb potential arises naturally from the correlation function of stochastic copying noise. Using the Martin–Siggia–Rose (MSR) path integral, we integrate out fast copying fluctuations and obtain an effective current–current interaction with a 1/r static propagator. The fine‑structure constant αQED is identified as a dimensionless ratio of the defect‑noise amplitude to the emergent quantum action scale ℏeff=a2/Δt, predicting its value from lattice geometry rather than postulating it. The Schrödinger equation emerges as the low‑energy projection of the stochastic copying operator L^copy onto the two‑defect sector. Energy levels En=−13,6/n2 eV are interpreted as spectral gaps between bound resonant modes and the scattering continuum. We further show that the proton radius puzzle follows from the finite defect correlation length ξdef, which modifies the potential at distances probed by muonic hydrogen. An analytic derivation of the Lamb shift sensitivity ∂(ΔE)/∂ξ∝ξ is provided, and dominant QED corrections are quantified at the ∼1,6% level. All predictions are sharply falsifiable by next‑generation precision spectroscopy and lattice simulations.