{"id":"W4385212506","doi":"10.1080/00029890.2023.2230836","title":"An Arithmetic Proof of a Theorem of Chan, Long, and Yang","year":2023,"lang":"id","type":"article","venue":"American Mathematical Monthly","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Carleton University","funders":"","keywords":"Mathematics; Arithmetic; Proofs of Fermat's little theorem; Discrete mathematics; Fundamental theorem; Compactness theorem; Fixed-point theorem","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":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.002556797,0.0004813785,0.001825506,0.0004727406,0.00009203034,0.00005262225,0.0007500754,0.0001579539,0.0005319034],"category_scores_gemma":[0.002318234,0.0004084301,0.0002692191,0.001728585,0.003865686,0.0001561712,0.0004250853,0.0004224314,0.0001854867],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00005357221,"about_ca_system_score_gemma":0.0001496478,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.00009301533,"about_ca_topic_score_gemma":0.0000237697,"domain_scores_codex":[0.9952995,0.0006423406,0.001362696,0.0006325676,0.001181116,0.0008818062],"domain_scores_gemma":[0.993789,0.003130681,0.000843753,0.001417787,0.0003396574,0.0004791929],"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":[0.0004443488,0.003205529,0.002232047,0.01141764,0.001255017,0.0001937958,0.02158966,0.00003144565,0.003369129,0.9448144,0.0007342491,0.01071273],"study_design_scores_gemma":[0.0007715882,0.002034317,0.001452011,0.001144184,0.0005370008,0.00002822517,0.01200441,0.04868279,0.008275152,0.9245049,0.00003045014,0.0005349353],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9317334,0.0002838729,0.01470563,0.0006742351,0.00005889655,0.001933952,0.0001718652,0.0001966952,0.05024148],"genre_scores_gemma":[0.9901014,0.00004977055,0.006501561,0.00003113866,0.00006293011,0.00006424627,0.0000117859,0.0001417031,0.00303546],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.05836803,"threshold_uncertainty_score":0.9998367,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0322801419233228,"score_gpt":0.3395447034063355,"score_spread":0.3072645614830127,"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."}}