{"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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":[],"category_scores_codex":[0.0005507867,0.0002289307,0.0003972095,0.0001185737,0.0004510949,0.00005903911,0.0004226772,0.00004044356,0.00629275],"category_scores_gemma":[0.0005866361,0.0002203934,0.0001445775,0.0002566376,0.0001215952,0.0001461003,0.0004348114,0.0002808378,0.0002425253],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001802353,"about_ca_system_score_gemma":0.00007805447,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000002879932,"about_ca_topic_score_gemma":0.000003376595,"domain_scores_codex":[0.9978477,0.00005724535,0.0006246928,0.0002660197,0.0008581622,0.0003461474],"domain_scores_gemma":[0.9979634,0.0009205975,0.000277576,0.0006547644,0.00008903272,0.00009462034],"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":[0.000004333519,0.0003920069,0.00002443756,0.0003001938,0.00004834862,0.00002132038,0.004695482,0.00001538422,0.0002822168,0.9467896,0.04738319,0.00004351625],"study_design_scores_gemma":[0.0003001158,0.00004277859,0.000002978219,0.00002693004,0.00005319866,0.000134413,0.003469412,0.001569383,0.00107376,0.9841099,0.008951068,0.0002660806],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"methods","genre_scores_codex":[0.2503017,0.000749129,0.2653173,0.007091788,0.001905418,0.004406406,0.001333592,0.002624759,0.4662699],"genre_scores_gemma":[0.3955731,0.0000271744,0.4645759,0.001477433,0.0002535721,0.001133205,0.00007441272,0.0003103597,0.1365748],"genre_candidate":"methods","genre_consensus":null,"teacher_disagreement_score":0.3296951,"threshold_uncertainty_score":0.9946156,"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."}}