Residual Structural Dynamics in Prime Gap Networks Under Iterative Condensation and Targeted Attack

Residual Structural Dynamics in Prime Gap Networks Under Iterative Condensation and Targeted Attack This work presents an experimental computational framework for investigating the structural behavior of arithmetic-derived networks under iterative condensation and targeted perturbation dynamics. Prime Gap Graphs, Fibonacci-derived graphs, and random control networks were analyzed through a residual structural operator and a targeted attack engine designed to progressively remove high-degree nodes while monitoring the evolution of modularity, assortativity, degree variance, and spectral localization (IPR). The experiments reveal qualitatively distinct behaviors among the analyzed domains. Prime Gap Graphs consistently exhibited persistent modular organization, sustained positive assortativity, and nontrivial spectral localization dynamics throughout the degradation process. A particularly notable phenomenon observed was temporary modularity reinforcement under directed attacks, where modularity increased before eventual collapse. In contrast, Fibonacci-derived graphs displayed highly ordered but fragile structures with rapid collapse under targeted perturbation, while random networks followed smoother entropy-driven fragmentation dynamics. The work does not claim universality or formal mathematical proofs regarding prime distributions. Instead, it introduces an exploratory computational framework for studying residual structural persistence phenomena in arithmetic-derived topologies. Included files: Full paper (PDF) Python simulation scripts Generated figures Experimental result tables Keywords:Complex Networks; Prime Gaps; Spectral Localization; Modularity; Targeted Attack; Residual Dynamics; Network Science