{"id":"W3037518341","doi":"10.1090/fic/060/07","title":"The ℓ-rank structure of a global function field","year":2011,"lang":"en","type":"other","venue":"","topic":"Advanced Differential Equations and Dynamical Systems","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Calgary","funders":"","keywords":"Rank (graph theory); Field (mathematics); Function (biology); Mathematics; Geography; Combinatorics; Pure mathematics; Biology; Evolutionary biology","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":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0000218532,0.0001145488,0.0001840818,0.0000119326,0.00003095777,0.0000081343,0.0001180075,0.0002048404,0.004243816],"category_scores_gemma":[0.000077627,0.00006073021,0.00007369944,0.00006035849,0.00002568705,0.000008710554,0.00002709106,0.00006924885,0.00001787476],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001414887,"about_ca_system_score_gemma":0.0000129256,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003998142,"about_ca_topic_score_gemma":0.003611246,"domain_scores_codex":[0.9994647,0.00002328647,0.0001875871,0.0001051404,0.0001255499,0.00009374188],"domain_scores_gemma":[0.9993545,0.000109798,0.0001986608,0.0002891205,0.00002436554,0.00002351655],"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":[0.0000142345,0.00001582785,0.00004267048,0.00006856606,0.00006861582,9.674186e-8,0.000005292344,1.302714e-7,0.00001625769,0.8362603,0.1578379,0.005670146],"study_design_scores_gemma":[0.0001966436,0.00007605147,0.00005409446,0.00009965531,0.00008864812,0.000001221353,0.00003415216,0.00006716031,0.00002057826,0.8668267,0.1323897,0.0001453928],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00004276408,0.0001446904,0.3615879,0.00001392143,0.0004756189,0.0002099343,0.00004561029,0.00007287974,0.6374068],"genre_scores_gemma":[0.07600388,0.00002890097,0.005796026,0.00003501839,0.0003242788,0.000009294087,0.00001439486,0.0001359776,0.9176522],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.3557918,"threshold_uncertainty_score":0.9966664,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01853725277359057,"score_gpt":0.280230769139566,"score_spread":0.2616935163659754,"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."}}