{"id":"W6958359436","doi":"10.6084/m9.figshare.19753978.v2","title":"[ARTICLE] An Exact Connection between π and the Golden Ratio φ (Canadian Journal of Mathematics Research / 2022)","year":2022,"lang":"en","type":"article","venue":"Figshare","topic":"Advanced Mathematical Theories and Applications","field":"Physics and Astronomy","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"","keywords":"Golden ratio; Connection (principal bundle); Unit circle; Expression (computer science); Function (biology); Constant (computer programming); Rotation (mathematics); Pentagon","routes":{"ca_aff":false,"ca_fund":false,"ca_venue":false,"about_ca":true,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.000673772,0.000259695,0.0004239355,0.001481923,0.00106623,0.002492628,0.0004926738,0.0004830435,0.01278573],"category_scores_gemma":[0.003265755,0.0002229429,0.0003627157,0.0009438921,0.003775083,0.002107836,0.001128547,0.001151555,0.001948105],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001762404,"about_ca_system_score_gemma":0.0006606332,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00436155,"about_ca_topic_score_gemma":0.003043283,"domain_scores_codex":[0.9994294,0.0001094543,0.0000251242,0.0001633967,0.0001947018,0.00007786851],"domain_scores_gemma":[0.9992903,0.0002055995,0.0001017241,0.00009262075,0.0002156074,0.00009401904],"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":[0.00001188898,0.000003084742,0.0001576341,0.00002405718,0.000002473498,0.00003756623,0.00009351284,0.0003904459,0.0007680827,0.9860832,0.002586644,0.009841355],"study_design_scores_gemma":[0.000007757142,0.00002077684,0.001484227,0.00002740221,0.000009010474,0.0003450996,0.00008834295,0.004367396,0.001653805,0.9476986,0.04427317,0.00002440303],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"other","genre_gemma":"empirical","genre_scores_codex":[0.149631,0.003936814,0.289564,0.003797896,0.001590898,0.00007526679,0.0004722582,0.0007914223,0.5501404],"genre_scores_gemma":[0.9213786,0.001471192,0.04372257,0.0005318596,0.0006938668,0.00005105679,0.0001297598,0.000458057,0.03156292],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.01278573,"threshold_uncertainty_score":0.04277253,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07405715661000993,"score_gpt":0.3457536324577332,"score_spread":0.2716964758477233,"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."}}