{"id":"W4414258789","doi":"10.2140/ant.2025.19.2163","title":"Geometry of PCF parameters in spaces of quadratic polynomials","year":2025,"lang":"en","type":"article","venue":"Algebra & Number Theory","topic":"Algebraic Geometry and Number Theory","field":"Mathematics","cited_by":1,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Toronto","funders":"","keywords":"Quadratic equation; Algebra over a field; Quadratic function; Difference polynomials; Connection (principal bundle)","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":[0.00113409,0.001073326,0.000982995,0.003934327,0.002714782,0.006058001,0.001875743,0.001470291,0.01060557],"category_scores_gemma":[0.002926107,0.0006600812,0.0006991483,0.002190493,0.004879297,0.007622829,0.003324647,0.003583226,0.001258159],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.002933554,"about_ca_system_score_gemma":0.000874489,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002751276,"about_ca_topic_score_gemma":0.001331331,"domain_scores_codex":[0.9984925,0.0003209223,0.00005722092,0.000338501,0.0004440861,0.0003467202],"domain_scores_gemma":[0.9984212,0.0004373387,0.0003032448,0.0001422326,0.0002874346,0.0004085079],"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":[0.00003537522,0.00001065738,0.0001514299,0.0000139863,0.000003563943,0.00005098596,0.0001712202,0.000545749,0.000251356,0.9966683,0.0003651542,0.001732273],"study_design_scores_gemma":[0.0000261733,0.00002873314,0.0004403534,0.00001004893,0.000006343708,0.0001699997,0.000193963,0.002618246,0.0004416585,0.9933154,0.002729899,0.00001912726],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.699456,0.001291485,0.1187289,0.003178778,0.0004612789,0.0001339242,0.001072188,0.0004080327,0.1752695],"genre_scores_gemma":[0.9782529,0.0003203483,0.007170571,0.0001692269,0.0003048598,0.00004115306,0.000340226,0.00009740226,0.01330329],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.01060557,"threshold_uncertainty_score":0.03547919,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.01845921413658844,"score_gpt":0.2991613124506696,"score_spread":0.2807020983140812,"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."}}