The Policy Distortion Factor Phi: Decomposing Routing Efficiency in Delay-Tolerant Networks

The realized delivery ratio of a delay-tolerant network factors exactly into three components: temporal reachability S_T, 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) Φ_rel < Φ_time 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.