{"id":"W4387327613","doi":"10.3792/pjaa.99.012","title":"Gosper’s strange series: A new, simplified proof and generalizations","year":2023,"lang":"en","type":"article","venue":"Proceedings of the Japan Academy Series A Mathematical Sciences","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"Toronto Zoo; Toronto Metropolitan University","funders":"","keywords":"Mathematical proof; Mathematics; Conjecture; Lemma (botany); Series (stratigraphy); Contiguity; Number theory; Pure mathematics; Algebra over a field; Combinatorics; Computer science; Geometry","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":[0.003104162,0.001024267,0.001097951,0.002563084,0.001767005,0.001953562,0.001514097,0.0008739891,0.005749987],"category_scores_gemma":[0.009393886,0.0003420108,0.001413145,0.002158472,0.005090415,0.007085286,0.003718851,0.004476722,0.0009919173],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001506944,"about_ca_system_score_gemma":0.0009714432,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007719134,"about_ca_topic_score_gemma":0.0006177,"domain_scores_codex":[0.9984758,0.0003516783,0.00009584388,0.0002542927,0.0007019753,0.0001202833],"domain_scores_gemma":[0.9978021,0.001074894,0.0001464601,0.0003135679,0.0004509976,0.0002120214],"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":[0.00001151331,0.000009359591,0.0001199334,0.00005771555,0.00000565917,0.0001784547,0.0002005953,0.000401026,0.0007674487,0.9900102,0.002061315,0.006176803],"study_design_scores_gemma":[0.000006805837,0.00001200156,0.0001714098,0.00003029492,0.000009401258,0.0003061216,0.00004986487,0.003443567,0.0009962443,0.9843247,0.01063241,0.00001710336],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.09046166,0.007822845,0.5956988,0.01310806,0.002941948,0.0001875462,0.0004905468,0.0008631841,0.2884253],"genre_scores_gemma":[0.8258088,0.007463741,0.1156871,0.003567541,0.005068135,0.0001799028,0.0003103312,0.0006606567,0.04125373],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.005749987,"threshold_uncertainty_score":0.01923567,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08616951326964999,"score_gpt":0.3389302790473279,"score_spread":0.2527607657776779,"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."}}