{"id":"W3125161437","doi":"10.5539/jmr.v13n1p41","title":"Some Remarks on the Relative Cohen-Macaulay Property","year":2021,"lang":"en","type":"article","venue":"Journal of Mathematics Research","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Commutative property; Property (philosophy); Invariant (physics); Formal power series; Power series; Pure mathematics; Finitely-generated abelian group; Discrete mathematics; Calculus (dental); Epistemology; Mathematical analysis; Mathematical physics; Philosophy","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.005749159,0.000149207,0.0003766008,0.0001953845,0.0004146674,0.0001356625,0.0006579116,0.00009052394,0.0005330982],"category_scores_gemma":[0.01029592,0.00007033827,0.000208609,0.0005871304,0.0002386839,0.0002141522,0.0002404242,0.00153105,0.0001499684],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001555746,"about_ca_system_score_gemma":0.0004032244,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001755219,"about_ca_topic_score_gemma":0.000004939666,"domain_scores_codex":[0.9964123,0.0007979773,0.0007556778,0.0001560409,0.001538095,0.0003399195],"domain_scores_gemma":[0.98611,0.01069342,0.0004012111,0.0007330651,0.001929782,0.0001325377],"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":[0.0000197412,0.0007730902,0.00001310861,0.0001103842,0.0001781026,0.00006574177,0.003143667,0.000002547076,0.003323182,0.9338006,0.05791387,0.0006559833],"study_design_scores_gemma":[0.0003069488,0.0001979548,0.00005964653,0.0003885742,0.00003770456,0.0001702921,0.002967048,0.0004020119,0.009680774,0.975944,0.009744236,0.0001008405],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6792003,0.002276668,0.0243875,0.1316653,0.0004401194,0.002507746,0.00003659779,0.00008014398,0.1594057],"genre_scores_gemma":[0.820897,0.001397729,0.1229879,0.0008356373,0.001486252,0.000161606,0.000004517391,0.0002183963,0.05201095],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1416967,"threshold_uncertainty_score":0.9980408,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2423736184141766,"score_gpt":0.4509349204153224,"score_spread":0.2085613020011458,"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."}}