The Metric Contraction of the Baryon: Precision Derivation of the Proton Radius Anomaly including Geometric Polarizability

We present a complete derivation of the proton radius discrepancy ∆rp = rμp − rep.We decompose the shift into a Leading Order (LO) static geometric shielding term and aNext-to-Leading Order (NLO) dynamic term arising from the Associator Polarizabilityof the vacuum. We demonstrate that while the static stiffness βQCD ≈ 1.91 accounts for−3.08% of the effect, the back-reaction of the muon on the non-associative geometry adds acorrection of −0.83%. The total predicted shift is ∆rAP H = −3.91%, in perfect agreementwith the experimental value of −3.92 ± 0.01%.