Galactic Rotation Curves as a Test Domain for Structuristics: Decompositional Integrity, Structural Regimes, and the Representation Limit of Baryonic Models

This paper tests three structural predictions derived from the Structuristics framework (Moura 2026, DOI: 10.5281/zenodo.19636897) on the SPARC dataset (Lelli et al. 2016), 175 galaxies and 3,391 data points, using galactic rotation curves as the empirical test domain. The formal mapping to Structuristics is exact: the observed rotation curve is the system behaviour, the baryonic decomposition into gas, disk, and bulge components is the Decomposition operator, and the composite baryonic velocity is the Construction operator output. Decompositional Integrity at each radial point is therefore I_D = Vbar/Vobs, a direct instantiation of the Structuristics metric in the galactic dynamics domain. Starting from the Radial Acceleration Relation (McGaugh et al. 2016) as the strongest known baryonic model (R2 = 0.877), a corrective model grounded in I_D with regime-specific weights is constructed and evaluated. All three structural predictions of Structuristics are confirmed: P1, the I_D radial profile exhibits three distinct structural regimes with empirically identifiable breakpoints; P2, regime parameters scale continuously with galaxy mass in a fractal-evolutionary pattern encoding mass assembly history; P3, structural groups show systematically different regime profiles, confirming I_D as a morphological invariant. A three-layer circularity audit (cross-validation, permutation test, and closed model without Vobs) confirms that the genuine non-circular gain is Delta R2 = +0.033, with R2_CV = 0.896 and permutation p = 0.000. The dominant residual signal is carried by the shape of the baryonic profile, not its amplitude, confirming the Structuristics distinction between Operator C (magnitude) and Operator D (spatial organisation). The residual gap Delta R2 = 0.064 is interpreted as the representation limit of Operator D in the projected rotation curve domain: the information destroyed by 2D projection of a 3D structure. Structuristics v2.0.0 establishes this as a formal consequence of Theorem D3 (non-injectivity of D), not merely an empirical observation. The gap is an empirical estimate of the organisational complexity K(y) for this domain, quantifying how much structural information about a galaxy is invisible to the projected baryonic Decomposition operator. The investigation followed the CAMAF operational protocol (Moura 2026, DOI: 10.5281/zenodo.20073205), which requires full traceability of the analytical chain, explicit declaration of non-claims, separation between empirical results and inference, and circularity auditing. AI tools (Claude, ChatGPT, Gemini) were used for script generation, diagnostic interpretation, and manuscript drafting; all scientific decisions were made by the author. See the Author Contributions section within the manuscript for the full declaration. Files included: galactic_curves_structuristics_v1_4_1.pdf (main manuscript), galactic_curves_structuristics_v1_4_1.tex (LaTeX source), references.bib (bibliography), and figures from tests T60v2, T98, T99, T101, T103 (PNG, 180 dpi).