ISF Paper I: Testing Quantized Dark Matter Fractions in the Phase Space Dimensionality Framework with SPARC Galaxy Rotation Curves

Testing Quantized Dark Matter Fractions in the Phase Space Dimensionality Framework with SPARC Galaxy Rotation Curves The phase space dimensionality framework — an extension of Radial Dimensionality Theory (RDT) — proposes that dark matter is ordinary matter in adjacent branches of a five-dimensional spacetime, gravitationally coupled through the bulk but electromagnetically confined to individual branes. This geometric interpretation predicts that dark matter mass fractions across galaxies should cluster at discrete values f_DM = (N−1)/N for integer branch count N, rather than the continuous distribution expected under ΛCDM. This paper presents the first systematic test of that prediction using 175 late-type galaxies from the SPARC database. Predictions were pre-registered at three nested tiers before examining the distribution shape: (A) statistically significant multimodality at (N−1)/N spacings, (B) a distribution mode near 5/6 ≈ 0.833 consistent with the cosmological anchor of N ≈ 6, and (C) an anti-correlation of f_DM with galaxy mass. Five independent statistical tests were applied — Hartigan's dip test, BIC-based Gaussian mixture model selection, Monte Carlo–calibrated BIC, Silverman's bandwidth test, and a targeted proximity test — along with three null models and 13 robustness variations. Result: The uniquely discriminating prediction (A) is not supported. BIC consistently prefers a single-component model (K = 1), and the distribution is well-described by a smooth beta distribution (KS p = 0.976). This result is robust across stellar mass-to-light ratio variations, quality cuts, morphological splits, radial extent restrictions, velocity bins, and bootstrap resampling. The weaker predictions (B, C) are supported but shared with ΛCDM and therefore not discriminating. The framework is not falsified — none of four pre-registered falsification criteria are triggered — but its unique signature is not detected in the current 175-galaxy sample. The forthcoming BIG-SPARC catalog (~4000 galaxies) is identified as the critical next test. Includes the compiled PDF. Version 2 Add public git repo with all analysis tools under active development with MIT License.