{"id":"W3127658947","doi":"10.1112/s0010437x23007455","title":"Lagrangian configurations and Hamiltonian maps","year":2023,"lang":"en","type":"article","venue":"Compositio Mathematica","topic":"Geometric and Algebraic Topology","field":"Mathematics","cited_by":10,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; Université du Québec à Montréal","funders":"Natural Sciences and Engineering Research Council of Canada; Courtois Foundation","keywords":"Mathematics; Lagrangian; Hamiltonian (control theory); Symplectic geometry; Pure mathematics; Hamiltonian mechanics; Disjoint sets; Mathematical analysis; Physics; Quantum mechanics","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001785813,0.0002655934,0.0002404252,0.001318484,0.001185284,0.001135483,0.0004337958,0.0004297516,0.003709758],"category_scores_gemma":[0.0008612014,0.0001955773,0.0001981608,0.0005561268,0.002025474,0.001927181,0.001324526,0.0005238042,0.000222778],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005854836,"about_ca_system_score_gemma":0.0002325555,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000776667,"about_ca_topic_score_gemma":0.000649735,"domain_scores_codex":[0.9998048,0.00003484272,0.000009695445,0.00003979323,0.00004973651,0.00006126365],"domain_scores_gemma":[0.9996901,0.00006777645,0.00008073407,0.00003943883,0.00003192861,0.00009017597],"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":[0.00003362972,0.00002076286,0.002224416,0.00003586289,0.00001005412,0.0005769967,0.000684845,0.004425757,0.004179726,0.9811372,0.0004931011,0.006177735],"study_design_scores_gemma":[0.00001888279,0.00004665909,0.002839195,0.00002154597,0.000008706487,0.0005415351,0.000906435,0.02153795,0.002186836,0.9693131,0.002559531,0.00001956885],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9653794,0.0002628684,0.01595605,0.000243072,0.00002420762,0.00001416057,0.00007207746,0.00005967203,0.01798863],"genre_scores_gemma":[0.9961391,0.00008088255,0.002108189,0.00001612999,0.00001834721,0.00001034861,0.00005805237,0.000007396617,0.001561495],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003709758,"threshold_uncertainty_score":0.0124104,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04256168120795402,"score_gpt":0.3060991930008699,"score_spread":0.2635375117929158,"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."}}