{"id":"W1832278448","doi":"10.1007/978-1-4757-3240-5_29","title":"Modular Equations and Approximations to π","year":2000,"lang":"en","type":"book-chapter","venue":"","topic":"Functional Equations Stability Results","field":"Mathematics","cited_by":349,"is_retracted":false,"has_abstract":false,"ca_institutions":"Simon Fraser University","funders":"","keywords":"Physics; Combinatorics; Algebra over a field; Mathematics; Pure mathematics","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":"codex-gemma-dda1882f352a","candidate_categories":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.0001783096,0.0002480399,0.0002779101,0.0002410019,0.0001553792,0.00005133091,0.0001138297,0.0002113328,0.004648855],"category_scores_gemma":[0.0005555211,0.0002426927,0.00008915552,0.000051783,0.00006314897,0.00008448815,0.00006286237,0.0001901626,0.001011971],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00009695994,"about_ca_system_score_gemma":0.00008277848,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00001255452,"about_ca_topic_score_gemma":0.00009614632,"domain_scores_codex":[0.9986609,0.0000126608,0.0004353826,0.0003902618,0.0003550128,0.0001457912],"domain_scores_gemma":[0.9982586,0.00079936,0.0000803579,0.0005603329,0.000164823,0.0001365427],"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":[0.000007432652,0.00002655296,2.161376e-7,0.0000347894,0.00003995982,5.537506e-7,0.0001249416,0.00009649195,0.000008930129,0.9942376,0.002344846,0.00307766],"study_design_scores_gemma":[0.0001259202,0.00003540495,0.000005606235,0.00004823709,0.0000674925,0.000004105587,0.00001013555,0.001613304,0.000003995448,0.8882228,0.1096253,0.0002377808],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"other","genre_scores_codex":[0.00005694169,0.00003345539,0.06393703,0.001349599,0.00005742908,0.0007993652,0.0001792341,0.0001689721,0.933418],"genre_scores_gemma":[0.001861629,0.0000190786,0.06087558,0.0002153913,0.0001185736,0.00008648691,0.0001416939,0.00006903969,0.9366125],"genre_candidate":"other","genre_consensus":"other","teacher_disagreement_score":0.1072804,"threshold_uncertainty_score":0.9997659,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08105823236318961,"score_gpt":0.2930869947484396,"score_spread":0.21202876238525,"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."}}