{"id":"W43428214","doi":"","title":"A Bijective Proof of an Identity Concerning Nodes of Fixed Degree in Planted Trees.","year":2000,"lang":"en","type":"article","venue":"Ars Combinatoria","topic":"Advanced Algebra and Logic","field":"Computer Science","cited_by":2,"is_retracted":false,"has_abstract":false,"ca_institutions":"","funders":"","keywords":"Mathematics; Bijection; Degree (music); Identity (music); Combinatorics; Discrete mathematics; Aesthetics","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":true,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0001971751,0.0001110127,0.0002649455,0.0001059539,0.00003708275,0.00001695863,0.0006213093,0.00005750961,0.00003971527],"category_scores_gemma":[0.00004867795,0.0001055372,0.00004347067,0.0005747883,0.00008492841,0.0008510906,0.00008179683,0.0001211665,0.000005000739],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003565094,"about_ca_system_score_gemma":0.00005560832,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0001709655,"about_ca_topic_score_gemma":0.000126037,"domain_scores_codex":[0.9989282,0.0001014687,0.0002881766,0.0002686256,0.0002199106,0.0001935875],"domain_scores_gemma":[0.9992907,0.00009621627,0.0001399533,0.0003538181,0.00007122645,0.00004807749],"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":[0.0001329926,0.0008283369,0.02526886,0.0000543194,0.0000409175,0.00007038031,0.004335384,0.001434646,0.005723789,0.8562925,0.00001869677,0.1057992],"study_design_scores_gemma":[0.002345476,0.0005432565,0.1596607,0.0001293056,0.000008228194,0.00001114264,0.000132869,0.01751468,0.04459625,0.7747598,0.00002749649,0.0002706902],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9957724,0.0001074374,0.002222276,0.00001758132,0.0001934996,0.0001525221,0.000003673026,0.00004175298,0.001488813],"genre_scores_gemma":[0.9977891,0.000006806116,0.002132578,0.0000171468,0.000002644228,0.000008373629,0.000002570362,0.000005896942,0.00003483114],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1343919,"threshold_uncertainty_score":0.4303681,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02417275242599681,"score_gpt":0.2655721328022063,"score_spread":0.2413993803762095,"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."}}