Information Fracture: A Mathematical Criterion for the Emergence of Autonomous Dynamical Regimes

Transitions between dynamical regimes are ubiquitous in physics, biology, and complex systems, yet no general mathematical criterion distinguishes ordinary phase transitions from the emergence of genuinely autonomous organizational structures. We introduce the concept of an information fracture: a threshold event in which coupled subsystems lose sufficient mutual information that the post-transition dynamics become structurally autonomous. The criterion combines three ingredients: (i) crossing of a control threshold, (ii) collapse of mutual information between interacting sectors, and (iii) emergence of a new vector field that cannot be continuously deformed from the pre-transition dynamics while preserving the original coupling structure. We formulate the definition independently of any particular physical realization and show how it can be operationalized within the Symbolic Finite Information Theory (SFIT), where local capacity saturation produces an information fracture associated with irreversible branching into a new dynamical sector. Numerical observables based on mutual information provide experimentally testable signatures of the transition. The framework offers a general mathematical description of the birth of autonomous dynamical organization applicable to physical, biological, and computational systems.