Sparse Law Companion Note: Extended Derivations, Escape Probability, and CGR Recovery

Extended derivations and proofs supporting the sparse law of deep-space DTN communication. Contains the escape probability model s ≈ s_base / (1 + p_touch · p_fail · s_base), CGR recovery analysis showing how Contact Graph Routing eliminates greedy dead-end losses, and semi-Markov ergodicity conditions for the CTMC efficiency model.

Provides calibration data for the s-predictor across six configurations (Mars 6-orbiter through cislunar 8-polar) and demonstrates CGR recovery factors at multiple heliocentric epochs.