{"id":"W4413035291","doi":"10.4153/s0008414x25101272","title":"Existence of ground states for free energies on the hyperbolic space","year":2025,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"advanced mathematical theories","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Simon Fraser University","funders":"Agencia Estatal de Investigación; Natural Sciences and Engineering Research Council of Canada; European Commission; Engineering and Physical Sciences Research Council; University of Oxford","keywords":"Mathematics; Hyperbolic space; Space (punctuation); Pure mathematics; Mathematical analysis","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":["metaresearch"],"consensus_categories":[],"category_scores_codex":[0.001100896,0.0002134664,0.0005998995,0.0002417748,0.0001680768,0.00005643236,0.0008646101,0.0000824114,0.00004596636],"category_scores_gemma":[0.01261996,0.0001376852,0.0001984425,0.0003266025,0.000386152,0.0001070784,0.00003939258,0.0002151613,0.000002939398],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001226593,"about_ca_system_score_gemma":0.0005935113,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006010082,"about_ca_topic_score_gemma":0.0008306307,"domain_scores_codex":[0.9983924,0.00005657783,0.0008331804,0.0001103514,0.0002674776,0.0003400315],"domain_scores_gemma":[0.9913918,0.006531705,0.0006346941,0.0006792512,0.0005804003,0.0001821096],"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":[0.00001283645,0.0000612154,0.000008115086,0.0006546346,0.0001090568,0.000006337172,0.00198858,0.00005812929,0.0001123157,0.9907035,0.006115436,0.000169816],"study_design_scores_gemma":[0.0003356012,0.000130883,0.000008424837,0.0009060794,0.0001156336,0.00002782662,0.005498747,0.0002300394,0.006392761,0.9833839,0.002849011,0.0001211171],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"methods","genre_scores_codex":[0.7731692,0.001184801,0.1947408,0.009125832,0.0008138285,0.001276452,0.0001993405,0.00004265407,0.01944711],"genre_scores_gemma":[0.4617914,0.00009190887,0.5330916,0.0005526115,0.0001977257,0.00005245633,0.000001725151,0.0001048133,0.00411571],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.3383508,"threshold_uncertainty_score":0.9956971,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0525486900001414,"score_gpt":0.3098548340299849,"score_spread":0.2573061440298435,"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."}}