{"id":"W4224305675","doi":"10.37236/10803","title":"Diagonal Hooks and a Schmidt-Type Partition Identity","year":2022,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"Dalhousie University","funders":"Killam Trusts; Michigan Technological University; Simons Foundation","keywords":"Mathematics; Diagonal; Partition (number theory); Combinatorics; Identity (music); Type (biology); Combinatorial proof; Discrete mathematics; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.001642111,0.0001143207,0.0002546556,0.00008353744,0.0003601054,0.0000513368,0.0003758087,0.0000258531,0.0001177388],"category_scores_gemma":[0.0005908508,0.0000870613,0.00008519714,0.0002851429,0.00008893337,0.0003328925,0.0002122548,0.0008366026,0.000004169637],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0003453192,"about_ca_system_score_gemma":0.0002065436,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000001816856,"about_ca_topic_score_gemma":0.000003530672,"domain_scores_codex":[0.9982969,0.0001928944,0.0004093371,0.0000849173,0.0006617053,0.0003542069],"domain_scores_gemma":[0.9985994,0.0005485344,0.0004272966,0.000190737,0.0001750432,0.00005903948],"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":[0.00004200486,0.0001353532,0.00007120029,0.00002928365,0.00006193459,0.000009398809,0.0003179088,0.00001569733,0.0001673058,0.9981983,0.0009030281,0.0000485784],"study_design_scores_gemma":[0.0004695873,0.0004775498,0.00006689851,0.00001402048,0.00009899528,0.0003497005,0.0005614896,0.00006230167,0.0002952595,0.9959208,0.001590412,0.00009296739],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9747599,0.00416769,0.01835097,0.0008795474,0.0005743834,0.0002012467,0.000001755573,0.00003419694,0.00103026],"genre_scores_gemma":[0.9982346,0.0003866052,0.00008617124,0.00004481987,0.0000676033,0.000007646613,4.348066e-7,0.00002067868,0.001151395],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.02347469,"threshold_uncertainty_score":0.3634669,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02832991252391726,"score_gpt":0.3128888972910232,"score_spread":0.2845589847671059,"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."}}