{"id":"W2157882570","doi":"10.37236/1802","title":"Partition Identities I: Sandwich Theorems and Logical 0&amp;ndash;1 Laws","year":2004,"lang":"en","type":"article","venue":"The Electronic Journal of Combinatorics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Waterloo","funders":"","keywords":"Partition (number theory); Mathematics; Combinatorics; Identity (music); Partition function (quantum field theory); Function (biology); Discrete mathematics; Physics; Quantum mechanics","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":[0.00308578,0.0003689,0.0005507229,0.001147851,0.002385656,0.003727741,0.00128406,0.001039901,0.006299936],"category_scores_gemma":[0.006233509,0.0004833139,0.001050541,0.000849363,0.006361818,0.006747655,0.003261122,0.002375833,0.0009804543],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002010375,"about_ca_system_score_gemma":0.0008786534,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0008639996,"about_ca_topic_score_gemma":0.0007153926,"domain_scores_codex":[0.9984093,0.0004323635,0.0001036341,0.0002761785,0.0005073605,0.0002710703],"domain_scores_gemma":[0.9974565,0.001248746,0.0002556853,0.0004731235,0.0002805809,0.0002853978],"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":[0.000003797194,0.000002612624,0.00006073123,0.000003949688,7.575464e-7,0.00001439305,0.00007508652,0.00005919362,0.0001277332,0.998495,0.0002106886,0.0009461054],"study_design_scores_gemma":[0.000006991872,0.000008529406,0.0001104464,0.000007596318,0.00000297298,0.00006727138,0.00006093876,0.001938621,0.0005598421,0.9947882,0.002441409,0.000007300049],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3309789,0.001186038,0.4842744,0.003397707,0.0004884201,0.0001251896,0.0002915739,0.0006562284,0.1786014],"genre_scores_gemma":[0.9184314,0.0003707162,0.0606236,0.0007802452,0.0003022618,0.0002088794,0.0001455217,0.0001535958,0.01898376],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.006299936,"threshold_uncertainty_score":0.02107543,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.03425596884997151,"score_gpt":0.3151625725292277,"score_spread":0.2809066036792562,"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."}}