{"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":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.002600363,0.000572554,0.0007775678,0.0002603019,0.0003873874,0.00011282,0.000870936,0.0003475969,0.03171565],"category_scores_gemma":[0.001554111,0.0004929269,0.0004013642,0.001205961,0.0003972912,0.0003505349,0.0004085238,0.0005928767,0.01394635],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00006471655,"about_ca_system_score_gemma":0.0000851106,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000009678121,"about_ca_topic_score_gemma":0.000002313262,"domain_scores_codex":[0.9960074,0.0008461989,0.0006582814,0.0007536621,0.0006849613,0.001049441],"domain_scores_gemma":[0.9924761,0.005783992,0.0002196097,0.001106227,0.0001004491,0.0003135923],"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":[0.0001540765,0.0002485767,0.03860887,0.0001583113,0.000817854,0.0001121105,0.005325194,2.06958e-7,0.0002482082,0.9032997,0.04512082,0.005906088],"study_design_scores_gemma":[0.0004441951,0.0001006594,0.01979105,0.0001320709,0.0001551883,0.00003848514,0.002094226,0.000003112815,0.002264659,0.9689733,0.00530356,0.0006995316],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9357059,0.0001014246,0.0006215812,0.0002607631,0.0005544191,0.0004029815,0.000143229,0.001245847,0.06096382],"genre_scores_gemma":[0.9803057,0.00002555763,0.0004114455,0.0002739181,0.0004062958,0.00007676429,0.0001089062,0.0001379613,0.0182534],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.06567357,"threshold_uncertainty_score":0.9997522,"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."}}