{"id":"W4409255786","doi":"10.1007/s10473-025-0413-2","title":"Proofs of conjectures on Ramanujan-type series of level 3","year":2025,"lang":"en","type":"article","venue":"Acta Mathematica Scientia","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Dalhousie University","funders":"","keywords":"Ramanujan's sum; Mathematics; Mathematical proof; Series (stratigraphy); Type (biology); Pure mathematics; Combinatorics; 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":[0.0047777,0.001850195,0.001763427,0.004229408,0.003250913,0.004488212,0.003458485,0.002435643,0.02608959],"category_scores_gemma":[0.02096438,0.0009007156,0.002290448,0.003049516,0.006576553,0.009402608,0.005339948,0.00768676,0.003163228],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.003065845,"about_ca_system_score_gemma":0.001443075,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001233352,"about_ca_topic_score_gemma":0.001070615,"domain_scores_codex":[0.9973417,0.0008878761,0.000137357,0.0003798859,0.0008245448,0.0004287102],"domain_scores_gemma":[0.9888862,0.007271354,0.0007124415,0.001072705,0.001183876,0.0008733396],"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":[0.00004991205,0.00003745634,0.0002477918,0.0001045674,0.00001350088,0.0001164186,0.0002455019,0.0006654331,0.0003121741,0.9896405,0.004366492,0.004200251],"study_design_scores_gemma":[0.00002166438,0.00001133152,0.0001562933,0.00002370877,0.000007507043,0.00006958706,0.00004776377,0.001904182,0.0002204151,0.9951162,0.00240983,0.00001136776],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.2446255,0.005898884,0.203018,0.02800683,0.005417443,0.0002048251,0.001348893,0.001549311,0.5099303],"genre_scores_gemma":[0.9059033,0.002851041,0.03760864,0.003326157,0.004847378,0.0002657305,0.001022167,0.000581349,0.04359433],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.02608959,"threshold_uncertainty_score":0.08727831,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07762561662803351,"score_gpt":0.3568986622679836,"score_spread":0.27927304563995,"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."}}