{"id":"W4391630212","doi":"","title":"Deficit and (q, t)-symmetry in triangular Dyck paths","year":2023,"lang":"en","type":"article","venue":"HAL (Le Centre pour la Communication Scientifique Directe)","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal; International Centre for Comparative Criminology","funders":"Institut national des sciences mathématiques et de leurs interactions; Agence Nationale de la Recherche","keywords":"Symmetry (geometry); Van Dyke beard; Combinatorics; Computer science; Physics; Mathematics; Political science; Geometry; Law","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":[0.00395615,0.0001355425,0.0002141616,0.0001918266,0.0001641475,0.0001091117,0.0003369483,0.00008703653,0.00007759632],"category_scores_gemma":[0.002054409,0.0001361443,0.00006046219,0.0007821917,0.00007689774,0.00006785652,0.0002296593,0.0001569861,0.00007885801],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00002768113,"about_ca_system_score_gemma":0.00003841158,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001099987,"about_ca_topic_score_gemma":0.0004578042,"domain_scores_codex":[0.9980865,0.0007945495,0.0003638475,0.0003062883,0.0002097432,0.0002390793],"domain_scores_gemma":[0.9963835,0.002214557,0.0001509136,0.0008812669,0.000277039,0.00009269724],"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":[0.000002428604,0.0003122363,0.001866956,0.0001392425,0.00001604473,0.000004598803,0.004651341,0.000001105122,0.001749765,0.9708377,0.005335982,0.01508263],"study_design_scores_gemma":[0.002814199,0.0000011312,0.01443048,0.001782715,0.00008334855,0.00003265771,0.001979921,0.05384008,0.02717142,0.8417545,0.05507871,0.001030854],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.90207,0.0002563004,0.03324281,0.008034385,0.00004032427,0.0005333969,0.00003196615,0.0003398744,0.05545095],"genre_scores_gemma":[0.9268996,0.0002699124,0.06299863,0.00004974436,0.00001122682,0.0001125838,0.00006185488,0.0000422069,0.009554231],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1290832,"threshold_uncertainty_score":0.5551801,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02934299328031256,"score_gpt":0.2700904534721678,"score_spread":0.2407474601918553,"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."}}