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.