The Policy Distortion Factor Phi: Decomposing Routing Efficiency in Delay-Tolerant Networks
Councilman, J.
Abstract
v5.1 (June 2026): Replaced the personal contact email in the author block with the project contact address ([email protected]). No other changes; data, figures, and 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. The realized delivery ratio of a delay-tolerant network factors exactly into three components: temporal reachability ST, a self-averaged Lyapunov chain exponent exp(E[H]λ), and a policy distortion factor Φ. This paper reports a 17,280-configuration sweep across eight solar system targets (Mercury to Titan) using both time-optimal and reliability-optimal oracles. Φ ranges from 0.3 to 8.6 and encodes the gap between oracle-predicted and simulation-realized routing efficiency. The reliability oracle universally reduces |Φ - 1| but does not eliminate the distortion, confirming that both objective mismatch and contact-graph topology contribute independently. Key findings: (1) Φrel < Φtime for all 8 targets. (2) σ-algebra separation rejected at 17k scale: distance leaks into Φ (ρ = 0.29). (3) Braess boundary: n=3 constellations show 89% Φ > 1 (diversity-dominated) while n=24 shows only 24% (dead-end tax). (4) n=6 is the universal crossover point.