Statistical Confirmation of the External Field Effect in SPARC Galaxies and Strict Limits on the Intrinsic Variation of the Acceleration Scale \(a_0\)

I present an independent, high-precision analysis of the Radial Acceleration Relation (RAR) using a sample of 161 galaxies from the SPARC catalog, combined with large-scale external gravitational field estimates. I confirm the External Field Effect (EFE) — a unique prediction of Modified Newtonian Dynamics — at a significance of 25.5σ, more than five times higher than previous reports. I measure a slope \(m = -0.700 ± 0.025\), in excellent agreement with theoretical expectations, and show that correcting for the EFE reduces the RAR residual dispersion by 62.5%. Model comparison via the Bayesian Information Criterion yields \( ≈ 6246\), decisively favoring the EFE over the null hypothesis. After controlling for the standard EFE contribution, I find no conclusive evidence for an intrinsic variation of the acceleration scale \(a_0\), placing a strict upper bound at the ∼5% level relative to the EFE amplitude.