Directional Baryonic Regulation in Disk Galaxies: A Density-Gated Extension to SPARC Scaling Relations

This paper introduces an empirical, density-gated extension to baryonic rotation-curve modelingthat reveals a previously unrecognized directional structure in the V ₁₀ₑ / V ₎₁ₒdiagnostic plane. Using the SPARC galaxy sample, we reproduce the observational framework of Starkman et al. (2018) and overlay physically normalized correction vectors predicted by Version 0. 3 of aminimal density-regulated model. The model employs a mass-scaled transition radius and alocal stellar surface-density proxy, with only a single bounded nuisance parameter per galaxyand a fixed global normalization shared across the entire sample. The resulting directional response field shows a coherent, surface-brightness–ordered pattern: low-surface-brightness disks experience the largest regulated shift toward saturation nearV ₁₀ₑ / V ₎₁ₒ 1, while high-surface-brightness systems remain largelyunchanged. This behavior reproduces the classical maximal-to-submaximal disk sequencewithout invoking halo profile tuning, modified force laws, or acceleration thresholds. A single figure compresses what would otherwise require extensive rotation-curve fitting into afalsifiable geometric constraint: viable models must reproduce not only the observed distributionof galaxies in the V ₁₀ₑ / V ₎₁ₒ plane, but also the direction of regulated evolutionacross surface-brightness regimes. This work is intended as an empirical organizing law rather than a definitive physicalmechanism. The same mapping could arise from modified dynamics, baryon–halo coupling, oreffective medium responses, and cosmological interpretation is explicitly deferred. Reproducibility and transparency are emphasized throughout. A companion Zenodo notebook provides a copy-paste, human-readable replication guide usingSPARC-style rotation-curve data and is cited in this record. This work builds on the Density-Dependent Braneworld Borrowing (DDBB) framework introduced in Zapresko (2026), applying its density-gated organizing principles to galactic rotation-curve diagnostics. The present paper focuses on empirical structure and falsifiable directional predictions, without relying on the microscopic or cosmological interpretations of the original framework. https: //doi. org/10. 5281/zenodo. 18296124