{"id":"W4396815879","doi":"10.48550/arxiv.2405.04638","title":"Additive triples in groups of odd prime order","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Rings, Modules, and Algebras","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Prime (order theory); Mathematics; Order (exchange); Combinatorics; Arithmetic; Business","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"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":[0.001051632,0.0006415536,0.0006765221,0.002498115,0.001607964,0.002071041,0.0005757355,0.0005789525,0.003374469],"category_scores_gemma":[0.003649338,0.0004018107,0.0006028478,0.001346946,0.002704343,0.002892501,0.001650951,0.001246174,0.0008069318],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001303812,"about_ca_system_score_gemma":0.0006590551,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000899332,"about_ca_topic_score_gemma":0.0007718891,"domain_scores_codex":[0.9988437,0.0002388975,0.00006753938,0.000208111,0.0003596004,0.0002822325],"domain_scores_gemma":[0.9976121,0.001213292,0.0004022148,0.0002323591,0.0003110391,0.0002290306],"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":[0.00009773601,0.00001747774,0.0005689127,0.0000554832,0.000007366684,0.0001659085,0.0004919333,0.002579598,0.002246433,0.980961,0.0008794047,0.01192866],"study_design_scores_gemma":[0.00001459202,0.00005248252,0.000511991,0.00002526225,0.00001486836,0.0002083008,0.0001634675,0.009584951,0.00314152,0.9794868,0.006772837,0.00002290542],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.6518536,0.001594206,0.2293265,0.001175152,0.0002979893,0.0001336188,0.0004166889,0.0005290681,0.1146732],"genre_scores_gemma":[0.965332,0.0007666551,0.02656913,0.0001460411,0.0002703398,0.0001218254,0.000232508,0.00004585136,0.006515593],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003374469,"threshold_uncertainty_score":0.0112887,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.08283338640033587,"score_gpt":0.2167409214262676,"score_spread":0.1339075350259317,"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."}}