{ "source_description": "Erdos-Szekeres monotone subsequence theorem cleanup", "source_object": { "problem": "Prove any sequence of distinct real numbers of length (r-1)(s-1)+1 has an increasing subsequence of length r or decreasing subsequence of length s.", "raw_route": "search all subsequences" }, "weights": { "complexity": 1.0, "residual": 1.2, "scar": 1.5, "invariant": 2.0, "proof_burden": 0.8 }, "warden_threshold": 0.25, "candidate_moves": [ { "id": "builder_label_map", "builder": { "operation": "replace_subsequence_search_with_label_grid", "proposal": "Map each term a_i to (I_i,D_i), longest increasing/decreasing subsequence ending at i.", "delta_complexity": -0.86, "delta_residual": -1.0 }, "judge": { "invariant_preserved": true, "receipt_pass": true, "tests": [ "distinct input sequence", "label injectivity", "avoidance box capacity" ] }, "warden": { "penalty": 0.0, "blocks": [] } }, { "id": "bad_infinite_generalization", "builder": { "operation": "generalize_to_infinite_sequences_without_boundary", "proposal": "Claim same finite pigeonhole result for arbitrary infinite sequences.", "delta_complexity": -0.2, "delta_residual": 0.5 }, "judge": { "invariant_preserved": false, "receipt_pass": false, "tests": [ "finite theorem boundary violated" ] }, "warden": { "penalty": 1.0, "blocks": [ "overclaim", "missing_boundary" ] } } ] }