{"id":"W4388198901","doi":"10.4064/aa220811-13-9","title":"Powers from products of terms in progressions with gaps","year":2023,"lang":"en","type":"article","venue":"Acta Arithmetica","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of British Columbia","funders":"","keywords":"Mathematics; Coprime integers; Prime (order theory); Product (mathematics); Term (time); Arithmetic; Arithmetic progression; Combinatorics; Discrete mathematics; Pure mathematics; Geometry; Quantum mechanics","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":[0.0006877584,0.001125703,0.0007067018,0.001126127,0.001573933,0.002659154,0.0009265569,0.0005755594,0.01565947],"category_scores_gemma":[0.002242561,0.0005659927,0.001149409,0.0008630925,0.003988255,0.005903631,0.003177184,0.002305415,0.004818713],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0007388904,"about_ca_system_score_gemma":0.000519622,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0002877525,"about_ca_topic_score_gemma":0.0005021275,"domain_scores_codex":[0.9991785,0.000137862,0.00005995113,0.0001684301,0.0002765007,0.0001788897],"domain_scores_gemma":[0.9993912,0.000188714,0.00009855779,0.0001333423,0.00009230153,0.0000958498],"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":[0.0001472436,0.00002242536,0.0003790819,0.0001394584,0.00001838467,0.0007171165,0.0007522476,0.0007627166,0.005389724,0.9777617,0.002009684,0.01190029],"study_design_scores_gemma":[0.000031184,0.00006554547,0.0005035974,0.00005881373,0.00002856683,0.000861618,0.0002674132,0.001690153,0.006490519,0.9687983,0.0211703,0.00003387811],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.472093,0.001603565,0.2073603,0.001473727,0.001028849,0.0001968982,0.0005856319,0.0008969594,0.314761],"genre_scores_gemma":[0.9068001,0.0008854599,0.03393517,0.0002504113,0.0006285567,0.0001092457,0.000384492,0.0005338947,0.05647268],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01565947,"threshold_uncertainty_score":0.05238616,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05125555906558191,"score_gpt":0.3531853051733564,"score_spread":0.3019297461077745,"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."}}