Lelli, Fraternali & Verheijen (2013) showed that the central circular-velocity gradient of disc galaxies, d_R V(0), scales with the central surface brightness as d_R V(0) ∝ Iu2080^0.55. This is close to the Iu2080^1/2 expected when the central dynamical density tracks the central stellar density. We examine how this relation, together with the baryonic Tully—Fisher relation (BTFR), appears in the two parameters (M, R) of the constant-Lagrangian (CL) rotation-curve model fitted to 175 SPARC galaxies.The inner branch of the CL curve is that of a homogeneous sphere to within the small Hubble term. The model gradient is therefore s_CL² ≃ GM/R³ (exact for H_z = 0) and the plateau speed is v_L² ≃ 3GM/R. The two relations are thus relations between photometry and the two combinations M/R³ and M/R.For 131 well-constrained galaxies, s_CL correlates with the 3.6 μm surface brightness at the innermost radius with Spearman ρ = 0.76 and a bisector slope of 0.45 (0.41—0.50). This lies inside the range 0.38—0.63 allowed by Lelli et al. (2013), while the ordinary and inverse regression slopes (0.35 and 0.56) bracket their value. Using the extrapolated exponential-disc central brightness instead lowers ρ to 0.58, as their analysis anticipates for galaxies with a central light excess.s_CL agrees in the median with the inner secant slope measured directly from the data (median ratio 1.01). v_L tracks the observed flat rotation speed V_flat to 0.03 dex, giving a BTFR scatter of 0.249 dex, against 0.226 dex with V_flat.A control analysis with the arctan rotation curve of Courteau (1997) yields the same correlations and slightly better fits. However, its central gradient is 38% above the measured secant slope, and its BTFR scatter is 0.297 dex.For the selected sample, combining the two relations predicts each rotation curve from baryonic quantities to within a typical factor of 1.25 (0.097 dex), equally well for both models. Refitting the CL model in velocity rather than squared-velocity space leaves the principal results essentially unchanged.The CL parameters thus encode both SPARC scaling relations with a direct physical reading, while the relations themselves are not unique to the CL form.This record contains the paper (LaTeX source and PDF), the Python scripts that reproduce every number, table and figure, the per-galaxy fit results, and the original SPARC tables (Lelli, McGaugh & Schombert 2016, AJ 152, 157). Code and data are archived at https://doi.org/10.5281/zenodo.23340027. An interactive explorer of the results is at https://haas2u-ai.github.io/bq-galaxy-models/models.html.