{"id":"W1498444635","doi":"10.4153/cmb-2008-015-6","title":"Numerical Semigroups Having a Toms Decomposition","year":2008,"lang":"en","type":"article","venue":"Canadian Mathematical Bulletin","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":11,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Mathematics; Modular design; Decomposition; Class (philosophy); Numerical semigroup; Semigroup; Pure mathematics; Algebra over a field; Chemistry; Artificial intelligence; Computer science","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0002082879,0.0001990568,0.0003036769,0.0001268179,0.0004186593,0.00003712905,0.000273474,0.0001069849,0.01689806],"category_scores_gemma":[0.0005076075,0.0001893214,0.0001186596,0.0002253728,0.0001371983,0.00004011762,0.00003413019,0.0002455851,0.009766767],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002086286,"about_ca_system_score_gemma":0.0001374717,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005430208,"about_ca_topic_score_gemma":0.0002821184,"domain_scores_codex":[0.9985836,0.00007386292,0.000384766,0.0002699064,0.0002252818,0.0004626054],"domain_scores_gemma":[0.9980846,0.0006963684,0.00007423965,0.0004485809,0.00008630755,0.0006098851],"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":[0.000008112862,0.000229662,0.0002957167,0.0001069934,0.0000523055,0.0001361978,0.00186589,0.000003699599,0.0002490868,0.8020766,0.1940141,0.0009616725],"study_design_scores_gemma":[0.0006585189,0.0001131893,0.002129459,0.0001897867,0.00008274215,0.001017303,0.0003902038,0.001737073,0.0008876161,0.8804777,0.1114541,0.0008623353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7625482,0.0001077503,0.0906046,0.01636551,0.00007603386,0.0009641994,0.00003861752,0.0003640563,0.128931],"genre_scores_gemma":[0.9759932,0.000005100296,0.02127822,0.0008878476,0.00008673279,0.0001160076,0.00001313333,0.00004591547,0.001573878],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.213445,"threshold_uncertainty_score":0.9910042,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04145802140227466,"score_gpt":0.3027654266228815,"score_spread":0.2613074052206069,"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."}}