{"id":"W2781050708","doi":"10.1016/j.jde.2017.12.018","title":"Degree counting and Shadow system for Toda system of rank two: One bubbling","year":2017,"lang":"en","type":"article","venue":"Journal of Differential Equations","topic":"Graph theory and applications","field":"Mathematics","cited_by":28,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of British Columbia","funders":"","keywords":"Degree (music); Shadow (psychology); Rank (graph theory); Mathematics; Point (geometry); Dirac (video compression format); Sequence (biology); Pure mathematics; Topology (electrical circuits); Combinatorics; Geometry; Physics","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":[0.0007070697,0.0001046556,0.0003846768,0.0001591441,0.0005927627,0.0001282307,0.0002824529,0.00005610831,0.00000908539],"category_scores_gemma":[0.0006473195,0.00008982993,0.0001687805,0.00005690445,0.00006854568,0.0002123766,0.00004517186,0.0001186114,0.000001003589],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003858711,"about_ca_system_score_gemma":0.00005456995,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001313208,"about_ca_topic_score_gemma":0.00002379259,"domain_scores_codex":[0.9987988,0.00005215053,0.0006890196,0.00009772783,0.000228947,0.000133379],"domain_scores_gemma":[0.9968857,0.0007374914,0.001522616,0.0003103883,0.0004732227,0.00007062887],"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":[0.00004140034,0.0001050567,0.0002085219,0.0007124836,0.0001518071,5.528119e-7,0.0002278712,0.00001007601,0.01624055,0.9814011,0.00003055647,0.0008700055],"study_design_scores_gemma":[0.01875344,0.0009433217,0.01162046,0.0109881,0.00614883,0.0002532658,0.008933725,0.08322757,0.03845933,0.8193347,0.0001874813,0.001149719],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5784675,0.000054719,0.4199947,0.0001015717,0.0002348271,0.0002831799,0.00003863636,0.00001560755,0.000809221],"genre_scores_gemma":[0.992318,0.000003527181,0.007317034,0.000001925501,0.0002661439,0.00001645063,0.000002431265,0.00001599984,0.00005848992],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4138505,"threshold_uncertainty_score":0.4559111,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1298811346104023,"score_gpt":0.3462757222627489,"score_spread":0.2163945876523466,"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."}}