A new mathematical framework inspired by a 100-year-old number theory can explain the movement of galaxies without needing dark matter at all.
April 29, 2026
Original Paper
A Universal Mass-Scaling Upgrade to the Ramanujan-Inspired p-Series Gravitational Framework
SSRN · 6467462
The Takeaway
Modern physics has spent decades searching for dark matter particles to explain why galaxies spin so fast. This paper uses a scale-invariant gravitational formula to show that the missing mass isn't an invisible substance. Instead, the math of gravity itself changes slightly as the mass of a galaxy increases. This framework matches the observed data across many different types of galaxies perfectly. If this holds up, it means the search for dark matter might be looking for something that isn't actually there.
From the abstract
We present a fundamental upgrade to the Ramanujan-inspired p-series deformation framework for gravitational interaction. While the original formulation successfully reproduced the empirical Radial Acceleration Relation (RAR) for individual galaxies, it failed to generalize across systems of widely varying baryonic mass. We resolve this Mass-Separation Problem through the introduction of the Nath Mass-Scaling Law R0(M) = α √ GM , where α ≈ 10 5 is identified as a universal scaling constant. This