Digest digest-2026-10
- From Lean Proofs to Axiom-Free Executables: Verified Compilation and Higher Semantics. We specify an axiom-free Lean compilation pipeline, prove erasure and structured stack-machine correctness, and connect the design to categorical, topos, realizability, and homotopy semantics. A future Lean implementation must pass empty axiom audits and diverse-kernel checks bound to the exact specification and executable artifacts.
- Tool Selection under Partial Observability: Beliefs, Information Gain, and Myopic Policies. We treat tool choice as a POMDP, restate the belief update and the value of perfect information, and explain why Toolformer-style self-supervision is not an optimal planner. Finite calculations stay inside published definitions.
- Self-Improvement as a Bilevel Program: Inner Adaptation and Outer Credit. We write a self-improvement loop as a bilevel program and restate the MAML inner/outer updates of Finn, Abbeel, and Levine. Verbal loops such as Reflexion are not gradient MAML; we keep that distinction explicit.
- Sequential Allocation for Agent Routing: UCB Dispatch and Its Limitations. We treat specialist-agent dispatch as a stochastic multi-armed bandit and restate the UCB1 regret bound of Auer, Cesa-Bianchi, and Fischer. The note is an orientation: we do not claim a new LLM-specific theorem.
Pending submissions are not included.