{"id":"W3198447119","doi":"10.48550/arxiv.2109.03440","title":"Pythagorean Triples in the Fibonacci Model Set","year":2021,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Mathematics and Applications","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"MacEwan University","funders":"","keywords":"Fibonacci number; Pythagorean triple; Fermat's Last Theorem; Pythagorean theorem; Counterexample; Diophantine equation; Mathematics; Ring (chemistry); Set (abstract data type); Combinatorics; Discrete mathematics; Algebra over a field; Pure mathematics; 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":"codex-gemma-dda1882f352a","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004284265,0.0002548195,0.0003566936,0.0001212333,0.0001065453,0.00008802108,0.0009221879,0.0002279928,0.0000713694],"category_scores_gemma":[0.0001045605,0.0002244233,0.0002239618,0.0003621175,0.00006062721,0.00006121959,0.0005570099,0.0005637199,0.00001749039],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00008544752,"about_ca_system_score_gemma":0.0001490783,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00006767365,"about_ca_topic_score_gemma":0.0003418319,"domain_scores_codex":[0.9987383,0.0001124056,0.000270316,0.0005360376,0.0001030154,0.000239853],"domain_scores_gemma":[0.9979551,0.0003835612,0.0002243682,0.001294728,0.00008237901,0.00005986666],"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":[0.000009511839,0.0004142936,0.0002029381,0.0004210337,0.00007766848,0.0001257602,0.003454797,0.06968999,0.00001776622,0.9130588,0.01246809,0.00005941998],"study_design_scores_gemma":[0.0002267271,0.000005306209,0.0000405847,0.0001046229,0.0001036901,0.00000368543,0.001751389,0.4761818,0.00002832453,0.5210159,0.0003007146,0.0002372505],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.8586246,0.00004343519,0.1162399,0.0003560402,0.00006165595,0.0007771351,0.0001007706,0.000101323,0.0236951],"genre_scores_gemma":[0.9932845,0.0001161202,0.003791905,0.00008394745,0.00004702566,0.000008678096,0.00006981142,0.00002689048,0.002571153],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.4064918,"threshold_uncertainty_score":0.9151717,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2933595587791839,"score_gpt":0.2561085016476074,"score_spread":0.0372510571315765,"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."}}