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

Abstract

This preprint develops Certified Autocatalytic Intelligence Theory (CAIT), an operational theory for measuring, certifying, attributing, and controlling reproduction of verified capability capital in AI R&D systems. It argues that AGI/ASI-relevant acceleration should be certified by net, endogenous, resource-normalized, safety-gated production of further verified capability capital rather than raw model capability, benchmark scores, candidate volume, or spectral reproduction diagnostics alone. The framework introduces typed partial certificate algebra, machine-readable registry and certificate records, domain witnesses, status-effect maps, evidence composition tables, window-balance certificates, operational metrics, and arrival decision rules. It separates endogenous reproduction from external injection, human assistance, tool upgrades, unresolved attribution, and unsafe or uncertified artifacts, making AGI/ASI arrival a certificate-relative lower-bound claim about verified capability-capital reproduction rather than hidden mental states or unrestricted deployment readiness.

Keywords

• Artificial intelligence
• verified capability capital
• capability-capital reproduction
• AGI
• ASI
• artificial general intelligence
• artificial superintelligence
• recursive self-improvement
• net endogenous growth
• certificate algebra
• domain witnesses
• evidence budgets
• anytime-valid inference
• confidence sequences
• causal attribution
• partial identification
• provenance
• deterministic replay
• AI R&D acceleration
• automated discovery
• service feasibility
• benchmark contamination
• AI governance
• AI evaluation

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