The Sparse Law of Deep-Space Communication: A Unified Theory of Feasibility, Efficiency, and Distortion for Cislunar and Interplanetary DTN

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 updated to AGPL-3.0-or-later. 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.

Establishes the three-factor sparse law DR = S_T × η_lyap × Φ for delay-tolerant network delivery ratio. Exact factorization validated across 154,000+ configurations spanning Mercury through Titan and four CRAWDAD mobility traces.