{"id":"W4386891276","doi":"10.2140/ant.2023.17.1789","title":"Differences between perfect powers: prime power gaps","year":2023,"lang":"en","type":"article","venue":"Algebra & Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":8,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Engineering and Physical Sciences Research Council; Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Prime (order theory); Prime power; Power (physics); Pure mathematics; Combinatorics; Physics","routes":{"ca_aff":true,"ca_fund":true,"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":[0.001416882,0.0005746512,0.0007434821,0.001432543,0.001198631,0.002536378,0.001159389,0.0008201614,0.009365348],"category_scores_gemma":[0.0103124,0.0004778201,0.0005662952,0.001074118,0.004031708,0.01062549,0.003229729,0.003520659,0.001462751],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0008289547,"about_ca_system_score_gemma":0.0004730106,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0003251831,"about_ca_topic_score_gemma":0.0002961917,"domain_scores_codex":[0.9987476,0.0001724796,0.00007458937,0.0003707769,0.0004407886,0.0001938874],"domain_scores_gemma":[0.9971936,0.001504109,0.0003276767,0.0005428909,0.0002156345,0.0002161005],"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":[0.00004379588,0.00001627757,0.0005765002,0.0000295543,0.000002985957,0.0001776227,0.0003609546,0.001573059,0.0005070022,0.9849584,0.0009413845,0.01081234],"study_design_scores_gemma":[0.000006786847,0.0000136403,0.0001003923,0.00001371146,0.00000311927,0.0001316112,0.00006655962,0.005261771,0.0006996279,0.9893589,0.004338217,0.000005554212],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.3499563,0.001338001,0.4851614,0.002587026,0.0008919513,0.00009268994,0.0003035985,0.0006495858,0.1590195],"genre_scores_gemma":[0.9495324,0.0004082783,0.03878694,0.0002327332,0.0003236963,0.00004763114,0.0001080112,0.000190264,0.01036991],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.009365348,"threshold_uncertainty_score":0.03133023,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.02957293754923262,"score_gpt":0.2950847403366215,"score_spread":0.2655118027873889,"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."}}