{"id":"W2096410438","doi":"10.7146/math.scand.a-14418","title":"Symmetry in the vanishing of Ext over Gorenstein rings","year":2003,"lang":"en","type":"article","venue":"MATHEMATICA SCANDINAVICA","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":91,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Metropolitan University","funders":"University of Kansas; National Science Foundation","keywords":"Mathematics; Finitely-generated abelian group; Local ring; Class (philosophy); Pure mathematics; Local symmetry; Symmetry (geometry); Ring (chemistry); Combinatorics; Geometry; Physics; Computer science; Chemistry; Particle physics","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":[0.001253596,0.0004270628,0.0006022298,0.00133626,0.001095631,0.002317881,0.0007879636,0.0005285109,0.00303109],"category_scores_gemma":[0.002346093,0.0002649758,0.0008779613,0.0005867743,0.003550631,0.004708661,0.002299963,0.001064714,0.0003764925],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007919631,"about_ca_system_score_gemma":0.000332268,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005231443,"about_ca_topic_score_gemma":0.0002817841,"domain_scores_codex":[0.9988559,0.0002593411,0.00008190428,0.0001987883,0.0002807536,0.0003232486],"domain_scores_gemma":[0.9986548,0.0004502706,0.0002866359,0.000152297,0.0001575023,0.0002983429],"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":[0.0001818735,0.00009283754,0.005204226,0.0001061335,0.00003209848,0.0009991971,0.001307904,0.002401475,0.008091779,0.9722651,0.0004922589,0.008825181],"study_design_scores_gemma":[0.00005206274,0.0001858248,0.004023206,0.00002484026,0.00004254358,0.001400736,0.0007841542,0.01464296,0.01039396,0.9661637,0.002231105,0.00005502488],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9616033,0.0002568685,0.02148613,0.0002329459,0.00003043472,0.00001753603,0.00005260032,0.00006139645,0.01625891],"genre_scores_gemma":[0.9968238,0.00009625806,0.001214803,0.00002653357,0.00003065586,0.000009809047,0.00004039194,0.0000133118,0.00174449],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.00303109,"threshold_uncertainty_score":0.01014006,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03066563130530035,"score_gpt":0.2995307009998782,"score_spread":0.2688650696945779,"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."}}