{"id":"W2037006863","doi":"10.1090/s1056-3911-04-00385-6","title":"Uniform bounds on multigraded regularity","year":2004,"lang":"en","type":"article","venue":"Journal of Algebraic Geometry","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":61,"is_retracted":false,"has_abstract":true,"ca_institutions":"Queen's University","funders":"","keywords":"Monomial; Mathematics; Pure mathematics; Variety (cybernetics); Homogeneous; Polynomial; Polynomial ring; Hilbert series and Hilbert polynomial; Discrete mathematics; Combinatorics; Mathematical analysis; Hilbert space","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":[],"consensus_categories":[],"category_scores_codex":[0.0006564942,0.0001791268,0.0003631956,0.0004530794,0.0001659724,0.0000569773,0.00040961,0.0001057012,0.0001623478],"category_scores_gemma":[0.0007791698,0.0001421361,0.0002482338,0.0006918227,0.00009860159,0.0002120233,0.00005549915,0.0005398673,0.00005483593],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001839973,"about_ca_system_score_gemma":0.0001483229,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000008197128,"about_ca_topic_score_gemma":0.00001071777,"domain_scores_codex":[0.9984194,0.00004433201,0.0006384413,0.0001374311,0.0005128895,0.0002474807],"domain_scores_gemma":[0.9981415,0.0004308189,0.0005641772,0.0004092245,0.0002794877,0.0001747422],"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":[0.00008489243,0.001088479,0.0004662958,0.00006139834,0.0002520789,0.00004340251,0.001073423,0.00005969008,0.002470445,0.9850908,0.004299067,0.005010012],"study_design_scores_gemma":[0.001877742,0.000536582,0.01392704,0.0001213734,0.00008188027,0.0002194137,0.0004114882,0.000009731433,0.01014057,0.9682497,0.004216479,0.0002079535],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9860016,0.0001365865,0.007198175,0.003217773,0.0001790606,0.0001425284,0.000005239045,0.00003290539,0.003086199],"genre_scores_gemma":[0.9825383,0.00002958025,0.01660357,0.0003256191,0.0002013238,0.000003411413,0.000001813255,0.00002513006,0.0002712838],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01684107,"threshold_uncertainty_score":0.5796142,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04373289924254106,"score_gpt":0.3261587176204097,"score_spread":0.2824258183778686,"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."}}