{"id":"W4417084325","doi":"10.48550/arxiv.2505.02605","title":"Cohen-Macaulay squares of edge ideals","year":2025,"lang":"en","type":"preprint","venue":"ArXiv.org","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Natural Sciences and Engineering Research Council of Canada; Dalhousie University","keywords":"Chordal graph; Bipartite graph; Square (algebra); Enhanced Data Rates for GSM Evolution; Graph; Finite set; Class (philosophy)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003829295,0.0003103367,0.0002541988,0.0009407412,0.0006882607,0.001205979,0.0003644917,0.0002907781,0.006299202],"category_scores_gemma":[0.001227219,0.000203879,0.0003097134,0.0004615068,0.001850566,0.001978785,0.001069198,0.0007738622,0.0007063161],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0004990817,"about_ca_system_score_gemma":0.0003186675,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0006084838,"about_ca_topic_score_gemma":0.0005339592,"domain_scores_codex":[0.9995657,0.00008710851,0.00002008182,0.0001065956,0.0001257023,0.00009477116],"domain_scores_gemma":[0.9992884,0.000269583,0.0001145221,0.00005321655,0.0001704798,0.0001038],"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":[0.00003766144,0.000008595204,0.0005243259,0.00002796391,0.000005439726,0.00008026941,0.0002250604,0.0007478943,0.002887166,0.990581,0.0006067129,0.004267903],"study_design_scores_gemma":[0.00001911846,0.00003582656,0.001005045,0.00001192977,0.000007552893,0.0002283748,0.0002773271,0.006250725,0.006572364,0.9750594,0.01051234,0.00001989856],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7503365,0.0006092811,0.1228266,0.0007146522,0.0001819955,0.00005374392,0.0004068973,0.000294743,0.1245755],"genre_scores_gemma":[0.9756956,0.0002059618,0.01383513,0.0001232141,0.00009118459,0.00004218836,0.0001824655,0.00004567971,0.009778528],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.006299202,"threshold_uncertainty_score":0.02107292,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1211806916030232,"score_gpt":0.3904649898244171,"score_spread":0.2692842982213939,"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."}}