Microscopic Derivation of the Policy Distortion Factor

Derives the policy distortion factor Φ of the three-factor sparse law from first principles via a competing-risk argument at each myopic routing decision. When inter-contact times follow a Pareto survival law with α < 1, the hazard function yields a scale-free balance between link commitment and contact rescue. The resulting closed form Φ = exp[−γ·E[H]·λ/(1+α·p_eff)] is a Lorentzian attenuation — a single-pole response function encoding the competition geometry. Validated on four CRAWDAD human-mobility traces (~47,000 configurations) with R² = 0.941. The running-coupling analysis reveals the Lorentzian acts as a resolvent: the asymptotic tail sector dominates the commitment integral while the body and hump of the inter-contact distribution renormalize the residuals.