Sparse Law Mathematical Primer: Three-Factor Decomposition, Lyapunov Self-Averaging, and the Policy Distortion Factor

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. Complete mathematical reference for the sparse law of deep-space DTN communication. Derives the three-factor decomposition DR =…