{"id":"W4309001212","doi":"10.3390/math10224251","title":"Is Catalan’s Constant Rational?","year":2022,"lang":"en","type":"article","venue":"Mathematics","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"York University","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Constant (computer programming); Catalan; Mathematics; Riemann zeta function; Euler's formula; Polynomial; Representation (politics); Riemann hypothesis; Function (biology); Pure mathematics; Proof of the Euler product formula for the Riemann zeta function; Catalan number; Rational function; Mathematical analysis; Algebra over a field; Arithmetic zeta function; Discrete mathematics; Prime zeta function; Computer science","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0008490899,0.0005289675,0.0006893635,0.001426575,0.001043841,0.004170003,0.001278234,0.0009402391,0.005119591],"category_scores_gemma":[0.004929738,0.0002013556,0.0004779728,0.0009289453,0.003910215,0.005193983,0.001038183,0.002204377,0.0009888696],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00192481,"about_ca_system_score_gemma":0.0009957227,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.003783867,"about_ca_topic_score_gemma":0.001947865,"domain_scores_codex":[0.9994707,0.0000721094,0.00001769613,0.0001262686,0.0001857207,0.0001275347],"domain_scores_gemma":[0.9991087,0.0003385903,0.0001001129,0.0001515135,0.0001967929,0.0001042205],"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":[0.000009315707,0.000003542669,0.0001911074,0.00001992758,0.000003130858,0.00005340546,0.0001001266,0.0002640455,0.0003106158,0.994822,0.0007320506,0.00349066],"study_design_scores_gemma":[0.000005826452,0.000008599301,0.0002491421,0.00003405932,0.000007464877,0.0001429809,0.0001244444,0.00424828,0.0007478849,0.9855676,0.008847537,0.00001623269],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.378801,0.009245967,0.1601476,0.015946,0.002552007,0.0000475032,0.0002170173,0.0004727893,0.4325702],"genre_scores_gemma":[0.967492,0.001940357,0.007750136,0.0006951461,0.0006649008,0.00001338338,0.00008840083,0.0001422982,0.02121327],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005119591,"threshold_uncertainty_score":0.01712674,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07257696533277556,"score_gpt":0.3346575901850152,"score_spread":0.2620806248522396,"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."}}