Agent-First Sanity: Sufficiency, Direction, and Receipts

We formalize necessary and sufficient conditions for an agent to certify its own sanity without external validation. The core insight is that sanity reduces to sufficiency arrows under guards: if an agent can verify its own receipts, maintain witness stability under perturbation, preserve meaning across translations, and demonstrate monotone improvement in its Murphy clock, then it possesses the minimal coherence required for trustworthy operation. We prove the Agent-First Sanity Theorem, establish compositional stability, derive tight deficiency–gap trade-offs, and show that confidence-based stopping via e-processes gives anytime validity. We augment the framework with complete proofs, computational complexity bounds, minimal sensor requirements, concentration inequalities for audit hashes, martingale analysis for confidence sequences, and expanded empirical validation with significance tests, confidence intervals, and ablations. No biconditionals are asserted; sufficiency arrows compose under guards.