{"id":"W7111623123","doi":"","title":"On Ramanujan's formula involving fifth powers of binomial coefficients","year":2024,"lang":"en","type":"article","venue":"Lirias (KU Leuven)","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Killam Trusts","keywords":"Binomial (polynomial); Binomial coefficient; Binomial distribution; Set (abstract data type); Power (physics); Term (time)","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0003670799,0.0002528475,0.0004279827,0.0002421689,0.00007762987,0.00009292892,0.0002998632,0.0001320772,0.0003506371],"category_scores_gemma":[0.001299044,0.0002201222,0.0002108911,0.0002975418,0.0001345874,0.0002853598,0.0001474322,0.000273959,0.0003090742],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001419978,"about_ca_system_score_gemma":0.00006226193,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001286219,"about_ca_topic_score_gemma":0.000009834992,"domain_scores_codex":[0.9981794,0.00004946582,0.0005515828,0.0003351798,0.0005080233,0.000376304],"domain_scores_gemma":[0.9977252,0.00149803,0.000130227,0.0004795326,0.00006870704,0.00009832577],"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":[0.00004829484,0.000237751,0.000006686576,0.001186958,0.00009129129,0.00004718974,0.002659272,0.0002059217,0.001062695,0.9844121,0.009272337,0.0007695523],"study_design_scores_gemma":[0.0005465136,0.0001912261,0.0000102353,0.001095152,0.00008372832,0.000009827791,0.000451461,0.005453668,0.00506632,0.9804063,0.006378981,0.0003066081],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9339764,0.0004965322,0.03724189,0.0003771089,0.002375068,0.0007797604,0.0000715004,0.0006437848,0.02403795],"genre_scores_gemma":[0.9840068,0.0000131204,0.006903777,0.00007231705,0.0001551126,0.00002512823,0.000008148031,0.00008574249,0.008729908],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05003034,"threshold_uncertainty_score":0.8976323,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.04458543134318455,"score_gpt":0.3421905962508639,"score_spread":0.2976051649076794,"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."}}