{"id":"W3147028298","doi":"10.5070/c63362791","title":"The combinatorics of a tree-like functional equation for connected chord diagrams","year":2023,"lang":"en","type":"article","venue":"Combinatorial Theory","topic":"Advanced Combinatorial Mathematics","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Bijection; Catalan number; Combinatorics; Mathematics; Chord (peer-to-peer); Algebraic number; Enumerative combinatorics; Diagram; Discrete mathematics; Computer science","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":["metaresearch","metaepi_narrow"],"consensus_categories":[],"category_scores_codex":[0.003204081,0.0003537081,0.0005853518,0.0001661113,0.0005883783,0.00006784279,0.0006319213,0.0002513616,0.00002027234],"category_scores_gemma":[0.01090721,0.0002813867,0.0003105072,0.001113198,0.0002921678,0.0001707857,0.0002078417,0.000280381,0.00003784244],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001683277,"about_ca_system_score_gemma":0.000155263,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001463661,"about_ca_topic_score_gemma":0.000001845235,"domain_scores_codex":[0.9969946,0.0003609387,0.0009158126,0.0003893823,0.0007452371,0.0005939903],"domain_scores_gemma":[0.9793751,0.01826068,0.0006308985,0.0008661521,0.0007407316,0.0001263972],"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":[0.0004715928,0.0002827174,0.00002582851,0.0001415495,0.0001270748,0.000001519569,0.0003157388,0.00001345701,0.0004639558,0.9893736,0.006686997,0.002095983],"study_design_scores_gemma":[0.003507399,0.0003552501,0.00005723607,0.00005857793,0.000111507,0.000002093958,0.0004307425,0.0009436539,0.002949657,0.9844411,0.0068357,0.0003070727],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.4339551,0.001005004,0.3663578,0.00138762,0.1600457,0.01351585,0.0002382132,0.004849306,0.01864545],"genre_scores_gemma":[0.9953329,0.00005968449,0.0008445259,0.00002289136,0.0007665831,0.0007026781,0.00007039066,0.0001429522,0.002057394],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.5613778,"threshold_uncertainty_score":0.9999638,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08863174281732114,"score_gpt":0.3230057342784626,"score_spread":0.2343739914611414,"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."}}