Self-advertised method selection lifts formal-proving hit@5 on Putnam from 84.2% to 95.0%

It separates method selection from similarity-based retrieval and shows formally that a similarity-only selector can assign the same representation to goals that need different methods, implying an information bound. Prior work retrieved facts, premises, or prior proofs and ranked by similarity; here the retrieval unit is a mathematical method carrying prerequisites, a target, an action, and residual obligations, with an information bound and a candidate-pool ceiling for two-stage selection. Given as formal propositions and proofs (Proposition 2, Corollary 1), noting that reranking baselines are bounded by the first-stage similarity pool, so a low-ranked annotated contract cannot be recovered by any reranking backbone at the reported shortlist sizes.

It introduces self-advertisement over 82 Method Contracts, each pairing an applicability description with Mathlib anchors, a checked scaffold or instance, and expected residual obligations, and elicits proposals for all contracts in one batched call. Unlike an LLM reranker that exposes only a score or ordering, self-advertisement makes each candidate commit to a target, action, and required conditions checkable against the goal, and a commitment gate demotes vague or unsupported main nominations to supporting roles. The 82 contracts are built from Putnam 2000–2014 solutions; every execution-side Lean artifact compiles under Lean v4.27.0 and Mathlib commit a3a10db, each contract provides a scaffold stated for arbitrary parameters and a compiled worked instance, and the authors reviewed every extracted method and proposed merge.

On Putnam 2015–2025 and IMO ProofBench, self-advertisement attains the highest recall@5 in all six backbone–benchmark settings, and on Putnam it also leads at hit@3, hit@5, and MRR under every backbone. Relative to lexical, dense-embedding, and embedding-plus-LLM-reranking baselines, the coverage gains come largely from methods that similarity ranks outside its top five, or that never enter the rerankers' candidate pool. With GPT-5.6 Luna, Putnam hit@5 is 95.0% and IMO ProofBench 91.7%, versus 84.2% and 88.3% for the strongest reranker; as the backbone moves from DeepSeek V4.1 Flash to GPT-5.6 Luna to GPT-5.6 Terra, Putnam hit@5 rises from .900 to .950 to .975 while the best reranker stays at .842, .842, and .858.

Adding the top-ranked contract to an Ax-Prover-style proof loop with a fixed compile budget raises the proportion of proved problems from 5.8% to 12.5% on Putnam and from 10.0% to 15.0% on IMO ProofBench. This is a first check of whether selected contracts help a prover, with gains concentrated in Putnam analysis and discrete problems and in IMO ProofBench Basic problems. Uses GPT-5.6 Luna with a budget of ten Lean compilations per problem; the comparison adds the selected contract as a whole, so it reflects selection and contract content together, and most problems remain unsolved within the budget.

The result targets formal proving with Lean and Mathlib: self-advertisement's checkable proposals and higher recall@5 are most useful when a prover tries shortlisted methods in order or needs to cover several methods from a reference solution. The contract library is built from Putnam 2000–2014 solutions and evaluated on held-out Putnam 2015–2025 and IMO ProofBench, so the intended setting is selection and reuse of competition-mathematics methods; execution-side scaffolds compile under Lean v4.27.0 and Mathlib commit a3a10db, and Proposition 1 states that instantiating a scaffold yields a checked proof once its required conditions and residual obligations have checked proofs.

Shortlist coverage does not guarantee a completed proof, the downstream comparison adds the contract as a whole rather than isolating selection from execution guidance, and most problems remain unsolved within the ten-compilation budget. Self-advertisement assigns each proposal an absolute score rather than comparing proposals directly, so scores from different contracts need not lie on a common scale, and the runoff compares only the leading proposals. Proposition 3's bound is conditional and worst-case, not a claim that the measured scores meet its premise; Proposition 4 shows expected hit@ is submodular when several methods apply, while the implementation sorts per-contract scores and does not run the greedy procedure. Labels were model-proposed and human-checked, so hit@ measures agreement with annotations, a conservative estimate of applicability.