{"id":"W4384997708","doi":"10.1016/j.aim.2023.109208","title":"Duality for asymptotic invariants of graded families","year":2023,"lang":"en","type":"article","venue":"Advances in Mathematics","topic":"Commutative Algebra and Its Applications","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":false,"ca_institutions":"McMaster University","funders":"Division of Mathematical Sciences; National Science Foundation","keywords":"Mathematics; Duality (order theory); Sequence (biology); Pure mathematics; Quotient; Algebraic number; Ideal (ethics); Reciprocity (cultural anthropology); Combinatorics; Mathematical analysis","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":[0.000558919,0.0001306264,0.0003545987,0.0001547668,0.00005798292,0.000009220291,0.0002570627,0.00004827375,0.00002479157],"category_scores_gemma":[0.001484031,0.0001170851,0.00006656799,0.0007093066,0.0001032439,0.0001742065,0.00007826239,0.00007580577,0.00001983868],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0000229311,"about_ca_system_score_gemma":0.00002778611,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001886139,"about_ca_topic_score_gemma":0.00002985591,"domain_scores_codex":[0.9988475,0.00003532831,0.00056018,0.0001614143,0.0001804687,0.000215054],"domain_scores_gemma":[0.9963104,0.002923108,0.000232229,0.0004103895,0.00009427162,0.00002959097],"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":[0.00000540338,0.0001846047,0.0004023734,0.00103088,0.00001669651,4.758967e-7,0.002471943,0.00003964243,0.000397278,0.9933054,0.000271272,0.001874004],"study_design_scores_gemma":[0.0003845217,0.00003357332,0.0008788407,0.0001284392,0.00002262637,0.000001313263,0.002021083,0.002061936,0.001438565,0.991819,0.001086158,0.0001239991],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.826784,0.0004900875,0.1556724,0.0003953486,0.0002405368,0.002386012,0.0001710217,0.000368118,0.01349248],"genre_scores_gemma":[0.7443292,0.0005835747,0.2538791,0.00003600393,0.000040246,0.0004809176,0.00002738322,0.00005405814,0.0005695292],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.09820665,"threshold_uncertainty_score":0.477459,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08095777763998267,"score_gpt":0.4013735934199422,"score_spread":0.3204158157799595,"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."}}