{"id":"W2098939570","doi":"10.1016/j.geomphys.2014.07.027","title":"Non-integrability vs. integrability in pentagram maps","year":2014,"lang":"en","type":"article","venue":"Journal of Geometry and Physics","topic":"Quantum chaos and dynamical systems","field":"Physics and Astronomy","cited_by":13,"is_retracted":false,"has_abstract":false,"ca_institutions":"Fields Institute for Research in Mathematical Sciences; Université de Montréal; University of Toronto","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Integrable system; Conjecture; Torus; Diagonal; Mathematics; Invariant (physics); Pure mathematics; Duality (order theory); Class (philosophy); Algebra over a field; Mathematical physics; Geometry; Computer science","routes":{"ca_aff":true,"ca_fund":true,"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":[0.0009353903,0.0001600452,0.000474063,0.00005027046,0.0000527624,0.00005328617,0.000163475,0.00004916643,0.00009980689],"category_scores_gemma":[0.0000300034,0.0001163083,0.0001992468,0.0002884173,0.00008542734,0.0002039984,0.00004499642,0.0004769226,0.00001142681],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003339992,"about_ca_system_score_gemma":0.00003138441,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002733624,"about_ca_topic_score_gemma":0.000005707464,"domain_scores_codex":[0.9987869,0.0001008413,0.0005322506,0.0001655714,0.0002014023,0.0002130559],"domain_scores_gemma":[0.9990615,0.0001957147,0.0002964101,0.0001879311,0.0001125984,0.0001458228],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"observational","study_design_scores_codex":[0.00009828913,0.0005541189,0.9092332,0.00007340262,0.00004659569,0.000001321493,0.0002344883,0.00007061202,0.0001958527,0.02784816,0.0003393446,0.06130459],"study_design_scores_gemma":[0.00393742,0.001455767,0.4793357,0.0004291066,0.0001019157,0.00001753543,0.0009177684,0.02714092,0.001418317,0.4730019,0.01144202,0.0008015773],"study_design_candidate":"observational","study_design_consensus":"observational","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9812743,0.00002530174,0.01533127,0.0001354596,0.0002874889,0.00009111404,0.00001469431,0.000003775365,0.00283657],"genre_scores_gemma":[0.9989479,0.000003266354,0.0002843296,0.00003400398,0.0006460348,0.000001967041,0.000005982981,0.000008634225,0.00006785759],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4451538,"threshold_uncertainty_score":0.4742916,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.007565794605121219,"score_gpt":0.2420800760023158,"score_spread":0.2345142813971946,"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."}}