Topological Bifurcation and Resilient Coherence in Super-Critical Networks: A Geometric Bound for Iterative Adaptation

We present a rigorous geometric derivation of the Maximum Geometric Plastic-ity Limit (k), defining the absolute mathematical boundary for structural adapta-tion in super-critical composite networks. Utilizing the Meta Invariant frameworkQE = (A/B)p, we evaluate the dynamic ratio balance between external compatibil-ity diffusion gradients and internal parity reconfiguration. By mapping this purelyarchitectural derivation to empirical observables, we provide a deterministic, scale-invariant mathematical framework that fully subsumes the empirical phenomena ofbiological adaptation, mass extinction, and speciation, reframing them as manda-tory topological consequences of geometric stress.