{"id":"W2124396273","doi":"10.1007/s00037-013-0064-x","title":"Lifting lower bounds for tree-like proofs","year":2013,"lang":"en","type":"article","venue":"Computational Complexity","topic":"Logic, programming, and type systems","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto; McGill University","funders":"","keywords":"Mathematical proof; Proof complexity; Mathematics; Constant (computer programming); Upper and lower bounds; Bounded function; Discrete mathematics; Sequent; Tree (set theory); Sequent calculus; Hierarchy; Combinatorics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.006001536,0.001770738,0.001702568,0.00441355,0.002350526,0.007252722,0.004725693,0.002324466,0.02783375],"category_scores_gemma":[0.04143658,0.001481061,0.003655128,0.004481421,0.004448295,0.02386352,0.009323793,0.01289965,0.004514235],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00457226,"about_ca_system_score_gemma":0.001799093,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001473251,"about_ca_topic_score_gemma":0.001859765,"domain_scores_codex":[0.9939907,0.001344069,0.0003253722,0.0009274349,0.002520445,0.0008920624],"domain_scores_gemma":[0.9584967,0.03011034,0.001319428,0.006324428,0.002338981,0.001410227],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.0001061812,0.00009638404,0.0004034328,0.0002477336,0.00003402048,0.00006324697,0.0002444541,0.005038374,0.0008201043,0.944762,0.009412957,0.03877101],"study_design_scores_gemma":[0.00001310508,0.00001577073,0.000116013,0.00005690182,0.00003215354,0.00003900818,0.00002711297,0.01122536,0.0004751718,0.9831951,0.004791582,0.0000126406],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.03683399,0.003525712,0.8564434,0.007915995,0.0008633519,0.0001822634,0.001085407,0.001435619,0.09171423],"genre_scores_gemma":[0.5877874,0.007393984,0.3521846,0.004011635,0.003923585,0.0007639491,0.003234597,0.00175587,0.03894445],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02783375,"threshold_uncertainty_score":0.09311318,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0681648188073247,"score_gpt":0.2876902495246916,"score_spread":0.2195254307173669,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}