A Universal Mass-Scaling Upgrade to the Ramanujan-Inspired p-Series Gravitational Framework

We present a fundamental upgrade to the Ramanujan-inspired p-series deformation frameworkfor gravitational interaction. While the original formulation successfully reproduced the empiricalRadial Acceleration Relation (RAR) for individual galaxies, it failed to generalize across systems ofwidely varying baryonic mass.Computational verification demonstrates that the upgraded model reproduces the observed RARacross several orders of magnitude in galaxy mass using only two universal parameters: the pseriesexponent p and the scaling constant α. The resulting framework provides a mathematicallyparsimonious alternative to Dark Matter interpretations of galactic dynamics.The discrepancy between observed galactic rotationcurves and Newtonian gravitational predictions has historicallybeen addressed through the hypothesis of ColdDark Matter (CDM). However, the tight empirical correlationknown as the Radial Acceleration Relation (RAR)indicates that baryonic matter alone strongly predicts theobserved acceleration of stars in galaxies.This remarkable regularity suggests the presence of anunderlying scaling law governing gravitational interactionrather than stochastic halo structures.In previous work we introduced a Ramanujan-inspiredgravitational kernel constructed from generalized p-seriesspectral structures. While this model reproduced theRAR for a reference galaxy, the framework encountereda critical limitation: the kernel scale parameter R0 remainedfixed.Because galaxies span several orders of magnitude inbaryonic mass, a static R0 cannot describe the full diversityof galactic systems. This paper introduces a massdependentscaling law that resolves this limitation.