{"id":"W4414053630","doi":"10.1007/s40687-025-00551-5","title":"The first level of $$\\mathbb Z_p$$-extensions and compatibility of heuristics","year":2025,"lang":"en","type":"article","venue":"Research in the Mathematical Sciences","topic":"Polynomial and algebraic computation","field":"Computer Science","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"American Mathematical Society","keywords":"Heuristics; Compatibility (geochemistry); Quadratic equation; Invariant (physics); Cyclotomic field; Prime (order theory); Quadratic field","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":[0.005510693,0.001190435,0.00210021,0.002444925,0.003631945,0.01166845,0.004925599,0.005106188,0.03056793],"category_scores_gemma":[0.0353502,0.001851147,0.003553748,0.002999099,0.007975343,0.02754499,0.008432495,0.0125619,0.004000624],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002850522,"about_ca_system_score_gemma":0.003252929,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002227942,"about_ca_topic_score_gemma":0.001483772,"domain_scores_codex":[0.9909176,0.00386779,0.0005865291,0.002129687,0.001381658,0.00111681],"domain_scores_gemma":[0.9726744,0.01591031,0.001226161,0.007713887,0.001432093,0.001043097],"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":[0.00003413106,0.00003234723,0.0002929907,0.00005691314,0.00001374569,0.00003893324,0.0002183625,0.0009322584,0.0002005128,0.991441,0.0007382093,0.006000612],"study_design_scores_gemma":[0.00001280248,0.00002728232,0.0001599076,0.00005159024,0.00001667946,0.00007973432,0.00009776812,0.005294212,0.0005372047,0.9875706,0.006134971,0.00001727941],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.06556896,0.001106185,0.7425608,0.006863926,0.0003010629,0.000232531,0.0006375341,0.001493378,0.1812356],"genre_scores_gemma":[0.6353678,0.0008789849,0.3370951,0.001874372,0.0004858377,0.0004231822,0.0008570721,0.001165272,0.02185249],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.03056793,"threshold_uncertainty_score":0.1022599,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.2974581575421071,"score_gpt":0.4421661870112759,"score_spread":0.1447080294691688,"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."}}