Lattice Field Medium Chi-Geometry as Dark Matter Alternative: Validation on SPARC Rotation Curves and Galactic Dynamics

This work presents a parameter-free kinematic reconstruction method (“chi-inversion”) derived from Lattice Field Medium (LFM) theory and applies it to galactic-scale dynamics. Using observed rotation curves as input, the method analytically reconstructs an effective scalar field χ(r) without per-galaxy tuning and tests 13 quantitative predictions against observational data. Validation is performed primarily on rotating disk galaxies using SPARC rotation curves (n = 175), complemented by SDSS velocity dispersion data (n = 1002), MaNGA IFU spectroscopy (n = 300), and the gravitational-wave event GW170817. Nine predictions are validated on real observational data with approximately 97–98% average consistency; four additional predictions are tested on synthetic or underpowered datasets and are identified as preliminary. The analysis is explicitly limited to galactic-scale kinematics and does not constitute a dynamical theory of gravity or a complete cosmological model. Elliptical galaxies, dwarf spheroidals, galaxy clusters, and cosmological observables (CMB, BAO, structure formation) are identified as critical untested regimes and are deferred to future work. This deposit corresponds to version 1.0 of the manuscript and is intended as a falsifiable, reproducible contribution to the study of galactic dynamics and dark-matter phenomenology. V1.1 Updates: Formatting and minor verbiage changes.