Proof-Carrying Cognition: Closing the Verification Gap with Reality-Settled Reward
Frontier gains in language-model reasoning come from reinforcement learning on reasoning traces and are concentrated in domains with a cheap, sound verifier. We argue the field's binding constraint is the verification gap: no scalable, incorruptible reward for reasoning outside formal domains. We make four contributions. (1) Theory: in a joint-Gaussian model of best-of-N selection, verifier-gold correlation rho is the exact exchange rate between test-time compute and capability, and an unsound verifier pays a polynomial penalty N^(1/rho^2); a margin-free copula form predicts realized soundness of real LLM judges to 4% median error. (2) Demonstration: in program-synthesis testbeds with exe...
| Authors | Eshwar Reddy M, Sourav Karmakar |
|---|---|
| Primary category | cs.AI |
| Published | 9 September 2026 |
| Last updated at source | 9 September 2026 |
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