Recursive Gravity: An Information-Theoretic Model of Galactic Rotation Curves with Emergent Saturation and Brittleness (N=50)

Description / Abstract We present Recursive Gravity, a purely baryonic, information-theoretic alternative to both ΛCDM and MOND. Treating galactic dynamics as a recursive gravitational interface, we define a dimensionless order parameter Ω(r) that quantifies structural retention relative to remaining adaptive capacity. Saturation is emergent (not hardcoded), arising from resolution limits in the recursive field, exactly as described in the companion paper Brittleness as Susceptibility in Recursive Systems. Brittleness is diagnosed not by high Ω, but by the susceptibility χ_Ω = |dΩ/dr|, which spikes near saturation, together with the participation ratio PR that signals information bottlenecks. A fully locked forward model (no per-galaxy tuning) driven solely by the baryonic scale length r_d is applied to 50 galaxies spanning the full SPARC diversity (dwarfs to high-mass spirals). The framework produces a tight geometric invariant κ (r96/r24) centered around 3–6, cleanly separates stable high-bulge systems (low χ_Ω, high PR) from brittle LSB/dwarf systems (early saturation spikes), and delivers competitive blind predictions of outer velocities (outer 25% of data hidden). Critically, it naturally predicts saturation-induced outer velocity softening — a falsifiable “kill shot” absent in standard MOND or dark-matter halo models. This deposit includes the complete analysis results (CSV), the emergent Python implementation, and supporting documents. The results demonstrate that many phenomena traditionally attributed to unseen mass or modified gravity can instead emerge from information-theoretic saturation and susceptibility in a recursive gravitational system.