{"id":"W2135248369","doi":"10.1007/s11139-015-9722-8","title":"A motivated proof of the Göllnitz–Gordon–Andrews identities","year":2015,"lang":"en","type":"article","venue":"The Ramanujan Journal","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Combinatorial proof; Algebraic number; Ramanujan's sum; Vertex (graph theory); Combinatorics; Algebra over a field; Pure mathematics; Graph","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00121841,0.001046602,0.0008835042,0.001629444,0.002161114,0.002325503,0.001878887,0.001807593,0.01616117],"category_scores_gemma":[0.00370914,0.000483324,0.001167012,0.001294689,0.003511182,0.003727657,0.003448133,0.003980718,0.002644975],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0015793,"about_ca_system_score_gemma":0.001037007,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001379899,"about_ca_topic_score_gemma":0.001533586,"domain_scores_codex":[0.9993502,0.000195586,0.00002762041,0.00009877205,0.0002377755,0.00008995767],"domain_scores_gemma":[0.9989377,0.0004766114,0.0000905362,0.0001906355,0.0001808583,0.0001237214],"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":[0.000003725797,0.000009137058,0.00003239662,0.00001684521,0.000002342794,0.00004151671,0.0000579948,0.0002023746,0.0002352163,0.9961016,0.001604793,0.001692029],"study_design_scores_gemma":[0.00000520485,0.000003938622,0.00008026729,0.000009433805,0.000002149074,0.00004608396,0.00001846732,0.001083538,0.0001073898,0.9943235,0.00431351,0.000006525538],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.128667,0.004509642,0.2546545,0.02522994,0.003419202,0.0001149573,0.0008923,0.0005076409,0.5820049],"genre_scores_gemma":[0.8464245,0.002600489,0.06858794,0.004714281,0.002397038,0.0001555251,0.0004264179,0.0003186656,0.07437518],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01616117,"threshold_uncertainty_score":0.05406451,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07542474400604823,"score_gpt":0.295775432009235,"score_spread":0.2203506880031868,"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."}}