{"id":"W4399714345","doi":"10.1007/s40993-024-00546-1","title":"Right-angled triangles with almost prime hypotenuse","year":2024,"lang":"en","type":"article","venue":"Research in Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"Université de Montréal","funders":"","keywords":"Prime (order theory); Combinatorics; Conjecture; Physics; 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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0007201161,0.0008043315,0.001037001,0.001528067,0.001675293,0.003277863,0.001471038,0.001382708,0.03265599],"category_scores_gemma":[0.004818459,0.0008295568,0.0007797679,0.001362327,0.002929625,0.004425549,0.003411313,0.003479018,0.006498214],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0005829078,"about_ca_system_score_gemma":0.000302157,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0005137143,"about_ca_topic_score_gemma":0.0004775437,"domain_scores_codex":[0.9983374,0.0003612555,0.0000915923,0.0004247641,0.000515206,0.0002697709],"domain_scores_gemma":[0.9971488,0.0009543776,0.000332966,0.0005828168,0.0006099748,0.0003711859],"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":[0.0001288745,0.00002040678,0.0002630005,0.00004138772,0.000009712739,0.0002478421,0.000233297,0.0005669376,0.002889245,0.9812601,0.002472053,0.01186716],"study_design_scores_gemma":[0.00004236654,0.00004156017,0.0003689382,0.00002139204,0.00001645106,0.0007859019,0.0002871916,0.003782807,0.003672401,0.970026,0.02093591,0.00001915943],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.2297273,0.0006646898,0.3962999,0.001512072,0.001960585,0.0001687901,0.0007488304,0.0008828723,0.3680349],"genre_scores_gemma":[0.8295668,0.0005303834,0.07470606,0.0007249914,0.0005655953,0.0001442084,0.0008779933,0.0009056928,0.0919783],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03265599,"threshold_uncertainty_score":0.1092451,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1421757856433499,"score_gpt":0.4467716674249849,"score_spread":0.304595881781635,"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."}}