Problemogenesis Theory: A Finite Proof-Carrying Audit Calculus for Problem-Frame Activation

Problemogenesis Theory: A Finite Proof-Carrying Audit Calculus for Problem-Frame Activation presents a formal framework for deciding when anomalies, failed requirements, retained traces, or proposed interventions may become valid problem frames for action. Instead of assuming that a problem is already given, the paper treats problem-frame activation as a finite, replayable audit process. The primitive object is a bounded envelope log: a structured record of sources, certificates, clocks, resources, risks, actions, and authority claims. A problem frame gains authority only when its evidence, certificates, obligations, read/write coverage, risk records, and resource permissions can be checked within a finite horizon. The framework gives conditions for deterministic replay, certificate liveness, problem-frame formation, safe patching, logged action provenance, finite risk control, non-hindsight novelty, and preservation under joins. The theory is intended for autonomous and semi-autonomous systems, AI research agents, scientific workflow tools, and safety-critical decision processes where actions should be tied to explicit evidence and reviewable authority. It also states clear limits: the calculus does not by itself prove external truth, physical effect, cryptographic security, statistical validity, or global optimality unless those assumptions are explicitly included in the trusted footprint.