Certified Autocatalytic Intelligence Theory: Net-Growth Certificate Algebra for Verified Capability Capital

This manuscript develops Certified Autocatalytic Intelligence Theory (CAIT), an operational theory for measuring, certifying, attributing, and controlling the reproduction of verified capability capital in AI R&D systems. The core thesis is that AGI/ASI-relevant acceleration should not be certified by raw model capability, benchmark scores, candidate volume, or a spectral reproduction diagnostic alone. Instead, acceleration is certified only when verified capability capital produces further verified capability capital after lifecycle status, provenance, evidence budgets, causal attribution, resource costs, obsolescence, service feasibility, transfer validity, evaluator integrity, and safety gates are applied. The paper formalizes CAIT as a typed partial certificate algebra for net, endogenous, resource-normalized, safety-gated growth. It introduces machine-readable registry records, certificate records, domain witnesses, status-effect maps, evidence composition tables, window-balance certificates, operational metrics, and arrival decision rules. The framework distinguishes endogenous reproduction from external injection, human assistance, tool upgrades, unresolved attribution, and unsafe or uncertified artifacts. It also treats product-window reproduction numbers as diagnostics rather than sufficient evidence for arrival-level acceleration. The resulting theory provides an auditable interface for determining whether a system exhibits sustained target-coordinate reproduction of verified AI R&D capability capital under explicit safety and evaluation boundaries. AGI/ASI arrival is treated as a certificate-relative lower-bound claim about verified capability-capital reproduction, not as a claim about hidden mental states or unrestricted deployment readiness.