Dark Matter Halo Fraction as a Predictor of Habitable-Zone Planet Occurrence: A Cross-Correlation Analysis Using SPARC Rotation Curves

We present a cross-correlation analysis between dark matter halo fraction (f_DM), derived from observed rotation curves in the SPARC database (175 disk galaxies, 3,391 kinematic data points), and a proxy for habitable-zone planet occurrence rate (eta_HZ) estimated via the established metallicity-planet scaling relation from Kepler survey data (Petigura et al. 2018). We report a significant negative correlation r(eta_HZ, f_DM) = −0.463 (p < 0.0001, N = 65), indicating that galaxies with higher dark matter fractions host stellar populations with systematically lower expected habitable-zone planet frequencies. In a multiple regression controlling for stellar metallicity (Z) and gas fraction (f_gas), the dark matter halo fraction retains a negative coefficient (beta_3 = −0.052), with the full model explaining R² = 0.788 of the variance in eta_HZ. While the incremental variance contributed by f_DM beyond metallicity and gas fraction is modest (ΔR² = 0.005), the consistent direction of the effect across all specifications is notable. We propose that this correlation reflects a causal chain in which the baryonic evolutionary state of a galaxy — quantified jointly by metallicity, gas depletion, and dark matter fraction — determines the demographic conditions for rocky planet formation. This represents the first systematic attempt to link galactic dark matter architecture to planetary habitability demographics using observational rotation curve data. We further situate this result within the Theory of Coherent Structures (TCS) framework, in which baryon-dominated galaxies correspond to nodes of maximum structural coherence in the galactic graph — the macroscopic analog of the low-friction stellar population identified in Gaia kinematic data.