Resolution of the Proton Radius Puzzle: Substrate Strain Polarization, Vacuum Impedance Stiffening, and the Preservation of Lepton Universality

The >7σ discrepancy between the proton electric charge radius determined from the Lamb shift in muonic hydrogen by the CREMA collaboration (r_p^(μ) = 0.84087(39) fm) and the CODATA consensus derived from electronic hydrogen spectroscopy and elastic e-p scattering (r_p^(e) = 0.8775(51) fm) constitutes the Proton Radius Puzzle. In orthodox quantum electrodynamics, lepton universality strictly dictates that the proton's spatial structure must remain invariant under lepton substitution. Resolving this anomaly within standard field theory has driven speculative proposals of unknown gauge bosons or fine-tuned nuclear polarizability cancellations. Building upon our foundational series on the physical vacuum as an elastically pre-stressed continuum, we show that the 4% radius discrepancy is the deterministic environmental consequence of localized substrate strain polarization. In our elastodynamic model, leptons are topological vortex solitons with rest-frame core stress scaling as P_ℓ ∝ m_ℓ^4. Because the muon orbits 186 times closer to the nuclear core (a_0^(μ) ≈ 284 fm), its immense internal stress (nearly nine orders of magnitude greater than that of the electron) nonlinearly hardens the vacuum shear impedance Z(σ) in the inter-soliton gap. This localized impedance stiffening deepens the Coulomb potential well, which—when analyzed through the conventional framework of a passive, linear vacuum—is misattributed to a 4% spatial shrinkage of the proton. We derive the analytical shift Δr_elasto^2 ≈ 0.063 fm^2, resolving the puzzle without violating lepton universality or introducing exotic gauge sectors.