Dynamical Regime Separation in Structure Preservation under rphys-Regulated Tearing on 3D Regge Lattices

We demonstrate a sharp dynamical regime separation between structure-preserving and structure-destroying regimes on three-dimensional Delaunay–Regge lattices with Sorkin–Newton–Raphson edge-length dynamics. The resolution-independent fracture criterion rphys [18]—an absolute physical displacement threshold—is compared against the standard strain-ratio threshold (Θ = 1.4) on blob-centered meshes (N = 5000, 9 seeds, 3000 Langevin steps) whose radial density gradient produces flat rotation-curve-like connectivity fields. The two criteria produce completely separated dynamical regimes with no overlap across seeds (Cohen's d = 83 on inner-shell retention, Mann–Whitney p < 4×10−4 on all metrics). Under rphys: the circular velocity profile vcirc(r) is preserved to within 1% (vpeak preservation 99.1 ± 0.1%, shape correlation r = 0.999), with alive fraction 0.996, inner shell retention 0.988±0.001, and connectivity field deviation DM3 = 0.159±0.073. Under the standard threshold: vcirc peak velocity is reduced by ∼34% (66.2 ± 1.7%), shape correlation collapses to r = 0.12, alive fraction drops to 0.874 ± 0.001, and inner retention to 0.654 ± 0.005. The standard threshold selectively destroys the dense inner core (shell S0 retention = 0.40) while leaving the outer periphery intact—a direct consequence of its mesh-dependent tear gap (Θ − 1) l0, which is smallest for the short edges of the dense core. The rphys criterion removes this geometric bias, preserving the radial structure that generates flat connectivity profiles. These results establish the dynamical bridge between boundary-localized curvature (Paper 2 [19]) and observationally competitive SPARC rotation curve fits (Paper 3 [20]): the radial density gradient that produces halo-like behavior survives rphys-regulated evolution on the same 3D Regge substrate used throughout the program.