MCMC Validation of the K-Kernel Framework on SPARC Observational Rotation Curves: A Dark Matter-Free Solution

This research provides a rigorous empirical validation of the non-local spatial and temporal memory framework (K-Kernel) applied to observed galactic rotation curves from the SPARC database, specifically targeting NGC3198. By analyzing the modeled Markovian spatial interpolation with a non-Markovian quantum memory integral, we accurately recover the observed flat rotation curve at large radii without invoking dark matter halos. Bayesian parameter estimation using Markov Chain Monte Carlo (MCMC) sampling yields remarkably tight posterior constraints on the Mass-to-Light ratio (M/L = 1.026), spatial decay rate (lambda_k = 0.116), and memory amplitude (k_amp = 17.49). These findings confirm that non-local spacetime memory offers a scale-invariant, statistically robust alternative to dark matter.