{"id":"W4385606160","doi":"10.1142/s1793042124500027","title":"Arithmetic progressions in squarefull numbers","year":2023,"lang":"en","type":"article","venue":"International Journal of Number Theory","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"Natural Sciences and Engineering Research Council of Canada","keywords":"Mathematics; Arithmetic; Conjecture; Divisor (algebraic geometry); Arithmetic progression; Variety (cybernetics); Prime factor; Prime (order theory); Property (philosophy); Number theory; Discrete mathematics; Combinatorics; Statistics","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":["insufficient_payload"],"consensus_categories":["insufficient_payload"],"category_scores_codex":[0.003375124,0.0001602649,0.0003138803,0.0005743318,0.00004296305,0.00007051275,0.0009811539,0.00009376881,0.00611821],"category_scores_gemma":[0.003047657,0.0001314278,0.0002306537,0.0005785204,0.0001632528,0.0002685895,0.000202311,0.0005460649,0.000853297],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0002280426,"about_ca_system_score_gemma":0.0001771355,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000006849891,"about_ca_topic_score_gemma":0.00001359379,"domain_scores_codex":[0.9970704,0.0004365494,0.0007803407,0.0001710717,0.001196431,0.0003451751],"domain_scores_gemma":[0.9960346,0.00264631,0.0003857443,0.0002273282,0.0005558161,0.0001501648],"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":[0.001118671,0.001047933,0.03966714,0.00007145161,0.0009985401,0.004807972,0.003739041,0.0000846046,0.0002936682,0.8213132,0.1014194,0.02543834],"study_design_scores_gemma":[0.001075879,0.00003932769,0.002170484,0.000393935,0.00002654802,0.0006848826,0.001573337,0.0002178475,0.0001562548,0.9849389,0.008562713,0.0001599111],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9354935,0.00005992107,0.002731109,0.003543291,0.001964225,0.0003241188,0.00009626619,0.00014839,0.05563913],"genre_scores_gemma":[0.9889868,0.00004169607,0.002881362,0.0001214668,0.0004578768,0.00001603551,0.00001220654,0.00005140218,0.00743115],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.1636257,"threshold_uncertainty_score":0.9999247,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.06374791328409778,"score_gpt":0.4271532786118919,"score_spread":0.3634053653277941,"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."}}