Certified Artificial Superintelligence Arrival from Typed Audit Logs

This manuscript develops a process-neutral, proof-carrying framework for certifying the arrival of artificial superintelligence under incomplete, fallible, and operationally messy evidence. Rather than defining ASI by benchmark scores, model scale, or a human-relative threshold, it formalizes ASI arrival as a layer-relative statement about sustained capability-producing trial generation, renewal, and viability across arbitrary processes, including models, scaffolds, laboratories, organizations, markets, software ecosystems, regulators, evolutionary systems, and coalitions. The framework introduces typed audit logs, compatible-history sets, certified random closed sets, a small proof kernel for bound certificates, abstract bound domains, typed decision semantics, identifiable coalition attribution, structural policy interventions, state-augmented hypergraph renewal processes, ordered ledger viability, evaluator noninterference, robust task coverage, and asymmetric three-valued decision rules. Certification requires sufficient evidence and strict dominance margins; rejection is permitted only from refuted necessary conditions. Missing or unreliable data widens uncertainty rather than becoming favorable evidence. The goal is to provide a mathematically explicit and implementation-oriented theory for evaluating self-improving AI systems, automated AI R&D, recursive capability feedback, agentic workflows, and broader sociotechnical capability-production processes in real environments.