We present Version 4 of the Density-Dependent Braneworld Borrowing framework with helical compactification (DDBB–HCEG), a geometric phenomenological framework in which gravity-like behavior, galaxy rotation-curve organization, and large-scale transport structure emerge from density-regulated circulation dynamics within constrained higher-dimensional geometry. The framework explores whether organized transport behavior, regulated by Hall-like circulation and global topological constraint, can account for several classes of large-scale dynamical phenomena without introducing additional dark-matter particles or direct modifications to Einstein gravity. In this interpretation, a four-dimensional observable manifold is embedded within a higher-dimensional bulk containing one warped extra dimension and one helically compactified dimension. At the brane–bulk interface, circulation pathways are constrained by figure-eight topology, producing bounded saturation behavior and density-dependent transport activation. High-density systems remain pressure-dominated and close to conventional localized gravitational behavior, intermediate-density systems develop regulated extended support associated phenomenologically with flat galaxy rotation curves, and low-density environments permit increasingly diffuse transport organization and rebound-like large-scale behavior. We connect this framework to empirical results from a companion SPARC analysis showing that galaxy rotation curves exhibit organized density-conditioned residual structure rather than purely random scatter about a single global relation. A minimal density-gated phenomenological model reproduces the qualitative ordering of rotation-curve behavior with effective surface density, while simplified toy systems naturally generate nonlinear saturation, hysteresis, thresholded activation, and long-lived coherent transport states. Controlled winding scans across odd helical windings m = 3–11 identify the m = 7 configuration as the most stable balance between coherent transport organization and saturation behavior within the explored toy-model class. Under a simplified odd-winding interpretation, this configuration additionally aligns with the observed three-generation fermion structure. The framework is presented as a falsifiable geometric and phenomenological interpretation rather than a completed microscopic theory. Its central proposal is that density-conditioned transport organization within constrained geometry may provide a unified structural lens for understanding multiple classes of large-scale dynamical behavior.
Matthew Zapresko (Thu,) studied this question.