{"id":"W7118052205","doi":"","title":"Thin Tree Verification is coNP-Complete","year":2025,"lang":"","type":"article","venue":"ArXiv.org","topic":"Complexity and Algorithms in Graphs","field":"Computer Science","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"K-ary tree; Interval tree; Tree (set theory); Graph; Segment tree; Gomory–Hu tree; Kruskal's algorithm; Spanning tree","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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0006504754,0.0004998176,0.0005449757,0.00039843,0.0009250334,0.0004623223,0.002682112,0.000254035,0.0004904993],"category_scores_gemma":[0.000134654,0.000554402,0.0003768597,0.002213506,0.0005174902,0.0007837408,0.0009207912,0.0006694639,0.001391772],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.000129251,"about_ca_system_score_gemma":0.0003623784,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002102984,"about_ca_topic_score_gemma":0.00004639022,"domain_scores_codex":[0.996119,0.0002551153,0.0008835969,0.001422989,0.0005160786,0.0008032596],"domain_scores_gemma":[0.9965563,0.0002990738,0.0003023157,0.002329116,0.000310188,0.0002029495],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"design_other","study_design_gemma":"observational","study_design_scores_codex":[0.0001077736,0.001083751,0.1601892,0.0003623554,0.0005811413,0.00007223133,0.008310886,0.00008594001,0.006702755,0.3879935,0.03677912,0.3977314],"study_design_scores_gemma":[0.001520895,0.000242483,0.5277847,0.0003931583,0.0001199559,0.00001376949,0.0002180369,0.2074154,0.008383131,0.03261879,0.2202833,0.001006355],"study_design_candidate":"observational","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4771408,0.004297063,0.4305157,0.03434572,0.01049121,0.001153633,0.0001023382,0.0006537953,0.0412997],"genre_scores_gemma":[0.9792339,0.0003705105,0.006349223,0.00638728,0.0002980328,0.00003845429,0.00001546757,0.00002243324,0.007284745],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.502093,"threshold_uncertainty_score":0.9996908,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0661122184933786,"score_gpt":0.2855311649564319,"score_spread":0.2194189464630533,"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."}}