A Phenomenological Lattice Tension Profile for Galaxy Rotation Curves: Application to the Full SPARC Sample

AbstractWe present a phenomenological dark matter density profile derived from a lattice tensionfunction Tₗattice (r) = T0/1+ (r/rₛ) ᵃlpha, and apply it to the full 175-galaxy SPARCrotation curve dataset using the Li+2020 baryonic decomposition. The resulting exponentialprofile rhoDM (r) = rhoₛ exp (-gamma r) has a cored inner structure and finite total halomass, avoiding both the NFW cusp problem and the need to choose between profilefamilies. Applied to all 175 SPARC galaxies, the model achieves a mean RMS of 3. 71 km/s (bootstrap 95% CI: 3. 31, 4. 15) and wins 146 of 175 head-to-head comparisons against theLi+2020 Burkert reconstruction (delta-BIC = -3, 669). An ablation study confirms that eventhe bare lattice tension profile (no geometric shielding, no central potential, no calibrationcorrections) outperforms the Burkert benchmark with mean RMS 5. 85 km/s and 126 wins. Asystematic floor audit confirms that all remaining residuals fall within the combinedobservational and systematic uncertainty envelope. Residual diagnostics reveal thatstubborn residuals organize into two structural families sharing a common reference spine, indicating that the remaining variance is structural rather than random. The physicalinterpretation of the lattice tension function in terms of an entropic substrate is deferred to acompanion theoretical paper (Brigo 2026a). Keywords: dark matter density profile, galaxy rotation curves, SPARC dataset, lattice tension, exponential halo, Burkert comparison, BIC, geometric shielding, residual diagnostics, systematicfloorAttribution note: The geometric shielding component of this model (Section 2. 3) was developed by thepresent author (G. Brigo) and is referred to as the Brigo Geometric Shielding (BGS) framework. Anearlier version of the full rotation curve architecture was published as a co-authored preprint underreference NKA-2026-001 (Martin, Lesperance and Brigo 2026), where the BGS framework is explicitlyattributed to the present author in Section II. B and in the Acknowledgments