Galactic rotation curves from topological void curvature: SPARC ts, prole diversity, and observational predictions

The curvature budget of topological voids in Regge calculus, without dark matter par-ticles or modified force laws, accounts for 83% of observed galactic rotation curves whileresolving the core-cusp problem and reproducing the Bullet Cluster mass-lensing offset.This is the most complete geometric alternative to particle dark matter tested against data.We fit the Gaussian void mass profile M(r) = Mtotal · P(3/2, r²/2R₀²) - derived fromGauss-Bonnet boundary curvature (companion paper [19]) - to 175 SPARC galaxies [9].The void framework exhibits profile diversity: a combined model (canonical Gaussian + tear-amplitude parameterization, both k = 2) accounts for 142 of 171 galaxies (83%) versus 18 forNFW (11%) in a three-way BIC comparison. A data-driven analysis (ρ ∝ r^β · exp(-(r/R₀)^γ), k = 4)confirms this diversity is physical: k-means clustering identifies four distinct profile familiesmapping onto the void/TEAR split (silhouette = 0.55), with high-mass cuspy galaxies (β ≈−1) favoring TEAR (72%) and low-mass cored galaxies (β ≈ 1) favoring the canonical void(97%).A stacked inner-residual analysis reveals a systematic +5.2% NFW velocity bias atr/Rdisk < 2 (the core-cusp signature, 82% of galaxies individually positive) while the voidmodel is nearly unbiased (−2.9%). Fisher information gives Neff = 0.99 - the void model iseffectively one-parameter. The Bullet Cluster mass-lensing offset is reproduced from geom-etry alone (3,816 severed edges, peak offset 0.0049). Five discrimination galaxies with SNRup to 5.2 provide concrete targets for IFS follow-up. The void radius scales as R0 ∼ M0.24bar(r = 0.46; bootstrap 95% CI [0.18, 0.39]), with a non-linear floor at Mbar 10⁹ M⊙ suggest-ing a minimum void size.