Deep-space communication networks operate under sparse, intermittent, and geometry-constrained connectivity. This work develops the Sparse Law, an exact factorization of end-to-end delivery ratio into structural feasibility and protocol efficiency: DR = STfull · η. Key results (v3): 7-configuration cislunar ablation study (31,500 bundles, 15 seeds, Bonferroni-corrected) CTMC efficiency bound: η0 = s/(s+1), confirmed at multiple operating points Mars cross-regime test: Mars relay (2-hop) yields η ≈ 0.97 vs cislunar (3–4 hop) η ≈ 0.68, confirming η0 is architecture-dependent — per-hop overhead δ accumulates over relay depth Contact-density sufficiency under renewal assumptions; non-ergodic degradation proved by construction Efficiency–feasibility anticorrelation under bounded-rationality routing Temporal percolation theory connections (directed percolation, event-graph mapping) Supplemented by the open-source TIN simulator and the percolation engine for Mars/cislunar DTN analysis.