Resolution-Independent Bond-Breaking Dynamics in Triangulated 2-Spheres via an Absolute Physical Length Scale

We introduce a resolution-independent fracture criterion for discrete simplicial manifolds, replacing the standard relative strain-ratio snap threshold with an absolute physical displacementcondition (rphys). Standard thresholds are pathological: the physical tear distance shrinks as N−1/2with vertex count, causing cascade dynamics to become artifacts of the discretization. The rphyscondition—analogous to the process-zone length of cohesive fracture models [10, 11]—defines an absolute gap below which bonds do not yield regardless of mesh density. We validate on a triangulated2-sphere across N ∈ {2000–20000} vertices with curvature defects, achieving RSM = 0.374 versusRSM = 0.792 for the standard approach (2.1× reduction in inter-scale dispersion). A constantdensity ensemble confirms fracture-rate invariance to 0.5% for N ≥ 5000. This 2D study establishesa scale-controlled foundation for dynamic topology in discrete spacetime models, with rphys actingas a nonlocal regularization length that remains finite as lattice spacing vanishes