Elastic Spacetime with Scale-Dependent Coupling (ESSC) v6.2 Radial Acceleration Residual Structure and the Emergence of a Characteristic Disk–Halo Transition Scale

Elastic Spacetime with Scale-Dependent Coupling (ESSC) v6. 2 investigates the radial structure of the residuals of the Radial Acceleration Relation (RAR) in disk galaxies. Using the SPARC galaxy database, this work analyzes how the logarithmic RAR residualDeltaRAR = ln (gₒbs) − ln (gRAR) varies as a function of the normalized radius R/Rd, where Rd is the exponential disk scale length of the stellar disk. By stacking the residual profiles across galaxies, the study identifies a coherent radial structure in the residual distribution. The analysis of the radial gradient of the stacked residual profile reveals the emergence of a characteristic transition radius in normalized disk units. This transition radius corresponds to a region where the gravitational contributions of baryonic matter and the dark halo become comparable. The results suggest that the residual structure of the RAR may encode information about the dynamical transition between baryon-dominated and halo-dominated regimes in disk galaxies. Within the ESSC framework, this transition scale is interpreted as a structural boundary associated with scale-dependent coupling between baryonic matter and the surrounding gravitational environment. The analysis emphasizes that ESSC is presented as a structural interpretation of the observed residual patterns rather than a modification of gravitational dynamics.