Information-Theoretic Extension of General Relativity: A Geometric Interpretation of Dark Matter Phenomena

Version 5.3: Revised from v5.2. Added metric axioms (positivity, symmetry, triangle inequality) for dobs with connection to Fisher information metric. Clarified observer-independence at macroscopic scales. Explicit statement of free-field approximation and general sourced case. Added observational constraint α A² ≈ 4.2 × 10⁸\,M_/kpc from NGC 3198. Added comparison with MOND and emergent gravity. References expanded with Wald (1984), Misner--Thorne--Wheeler (1973), Amari & Nagaoka (2000), and Begeman et al. (1991). This version is the consolidated release of the v5 series.