Microscopic Derivation of the Policy Distortion Factor

v5.1 (June 2026): Resolved the unresolved citation placeholders (References section added), updated the author contact email to research@percolate.space, and aligned the cited classification work to its current title (framework). Results unchanged.

v5.0 (March 2026): Revised terminology and epistemic framing throughout. Definitional identities relabeled as Propositions. Classification language updated. Mechanism descriptions qualified as proposed interpretations. License: CC-BY-4.0 (revised from the earlier AGPL-3.0-or-later statement). Scientific conclusions unchanged.

v4.0 (March 2026): Revised for consistency with classification theorem v7.0. Demoted empirical results from Theorem to Observation/Conjecture. Corrected gamma normalization convention. Updated DOI cross-references to concept DOIs. Added self-DOI to author block. Qualitative conclusions unchanged.

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.