{"id":"W2014991120","doi":"10.1007/s11856-011-0170-x","title":"Sums and products along sparse graphs","year":2011,"lang":"en","type":"article","venue":"Israel Journal of Mathematics","topic":"Limits and Structures in Graph Theory","field":"Mathematics","cited_by":14,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Combinatorics; Disjoint sets; Upper and lower bounds; Product (mathematics); Matching (statistics); Discrete mathematics; Generalization; Mathematical proof","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":[0.001221308,0.0002134748,0.0004798093,0.0002112057,0.0001298395,0.00003043551,0.0003412237,0.0001005406,0.0000405537],"category_scores_gemma":[0.000818673,0.0001468346,0.0001381297,0.0001668255,0.0001929767,0.0001614106,0.0001110958,0.0002997394,0.000003077643],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00001359401,"about_ca_system_score_gemma":0.00003756319,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000004258901,"about_ca_topic_score_gemma":0.000004641917,"domain_scores_codex":[0.9983668,0.00006893097,0.0008091002,0.000133561,0.0003775287,0.0002441194],"domain_scores_gemma":[0.9981139,0.0003194538,0.0007526259,0.0003781923,0.0002997804,0.0001360851],"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":[0.00003627124,0.0003210311,0.002592089,0.0004743394,0.0002050534,0.0001120513,0.01347457,2.487242e-7,0.0003743444,0.9795997,0.001003291,0.001806998],"study_design_scores_gemma":[0.0004756779,0.0001693824,0.001123066,0.0001961701,0.0001851131,0.001340545,0.002388473,0.0000169403,0.003392701,0.9902561,0.0002645298,0.0001912999],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9928702,0.0005792597,0.001320484,0.00006162783,0.0004432699,0.000161211,0.000003246408,0.00002666462,0.004534019],"genre_scores_gemma":[0.8325422,0.0001367177,0.1669664,0.0000614555,0.0001221517,0.000001335755,1.557977e-7,0.00003723831,0.0001322421],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.165646,"threshold_uncertainty_score":0.5987742,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.078044364158453,"score_gpt":0.2790261313142098,"score_spread":0.2009817671557568,"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."}}