{"id":"W4411279071","doi":"10.1112/mtk.70029","title":"Arithmetic constants for symplectic variances of the divisor function","year":2025,"lang":"en","type":"article","venue":"Mathematika","topic":"Analytic Number Theory Research","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Université de Montréal","funders":"Division of Mathematical Sciences; Natural Sciences and Engineering Research Council of Canada; Centre de Recherches Mathématiques; London Mathematical Society; National Science Foundation","keywords":"Mathematics; Symplectic geometry; Divisor (algebraic geometry); Divisor function; Symplectic matrix; Matrix (chemical analysis); Function (biology); Field (mathematics); Random matrix; Connection (principal bundle); Algebra over a field; Pure mathematics; Symplectic representation; Moment map; Geometry","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":[],"consensus_categories":[],"category_scores_codex":[0.0007210891,0.0001102953,0.0002650921,0.00009156069,0.0001143239,0.00002266575,0.0003019164,0.00005407918,0.0003857593],"category_scores_gemma":[0.001621925,0.00007194825,0.0001274668,0.0003973347,0.0001590123,0.00003625943,0.00009638632,0.00008225681,0.00002374405],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.00003547549,"about_ca_system_score_gemma":0.00008506738,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000003794032,"about_ca_topic_score_gemma":0.00001358141,"domain_scores_codex":[0.9990202,0.00008573943,0.0003063311,0.0001658967,0.0002205661,0.0002012377],"domain_scores_gemma":[0.997732,0.00151249,0.0001501821,0.0004685429,0.000112589,0.00002413449],"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":[0.00002762362,0.0001210663,0.0004202365,0.0006556464,0.0001282266,1.740304e-7,0.0001422604,8.780065e-7,0.0004227558,0.9924903,0.004658743,0.0009321013],"study_design_scores_gemma":[0.0004295555,0.0000276849,0.0002467599,0.0002405166,0.0001365954,0.000002600084,0.0002329442,0.001046303,0.001970636,0.9945588,0.0010383,0.00006930367],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"methods","genre_gemma":"empirical","genre_scores_codex":[0.05231642,0.000168467,0.667031,0.0009143081,0.0004038578,0.002194587,0.00002729275,0.0001452092,0.2767988],"genre_scores_gemma":[0.9350116,0.000002543073,0.006600108,0.00005717212,0.00002372659,0.0001230734,5.025452e-7,0.00003338005,0.05814788],"genre_candidate":"empirical","genre_consensus":null,"teacher_disagreement_score":0.8826952,"threshold_uncertainty_score":0.4223794,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.05841303826825014,"score_gpt":0.3652095132154852,"score_spread":0.3067964749472351,"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."}}