Escape Probability and the Heterogeneity Penalty in Custody-Based Deep-Space Networks

Companion note to 'The Sparse Law of Deep-Space Communication.' Tests whether the CTMC efficiency parameter s = η/(1-η) is universal or architecture-dependent across 24 configurations spanning Mars and cislunar relay networks with 2-4 relay hops. The parameter s separates into two regimes: ISL-free networks (s ≫ 1, η → 1) where routing decisions are forced, and ISL-connected networks (s ~ 2-70) where inter-satellite links generate dead-end ambiguity that greedy forwarding cannot resolve. ISL presence is the dominant factor, dropping s by 10× at matched hop count — a larger effect than adding a relay layer.