Barrier Capsule Dichotomy and Forced Cleavage

We establish a dichotomy governing recombination in admissible configuration classes. Either admissibility is stable under localized recombination, or there exists a localized quantitative obstruction—termed a barrier capsule—that enforces a uniform defect gap under adversarial recombination. We further show that such obstructions may be extracted constructively via forced-cleavage pairs, paralleling selective bond-cleavage techniques used in chemistry to expose latent structural weaknesses. The result isolates a precise and quantitative mechanism by which global equivalence fails despite local admissibility. This work was developed through sustained human–AI collaboration with ChatGPT (OpenAI). The core theorem, definitions, and proof architecture were formulated through iterative mathematical dialogue. All mathematical claims and formal responsibility remain with the human author.