ESSC v6.5 — Residual Structure in the Radial Acceleration Relation and a Radial Transition Band in Disk Galaxies

This work analyzes the residual structure of the radial acceleration relation (RAR) using the SPARC galaxy rotation curve database. After accounting for the leading dependence on halo fraction, a weak but persistent radial structure remains in the RAR residuals. The residual pattern forms a broad transition band around R/Rd ≈ 2.5–3.5 across the disk galaxy sample. The analysis indicates that the apparent tightness of the RAR does not eliminate all internal dynamical structure. Instead, a secondary radial organization appears once the dominant halo contribution is removed. The numerical value π lies within this transition band. This observation is presented as a geometric coincidence rather than evidence of a new dynamical constant. This study does not propose a modification of gravity or a new physical law. The goal is to document a potential internal radial structure in the RAR residual field and to provide a descriptive observational analysis of this feature within the SPARC galaxy sample.