{"id":"W4401661952","doi":"10.48550/arxiv.2407.11476","title":"Fay identities for polylogarithms on higher-genus Riemann surfaces","year":2024,"lang":"en","type":"preprint","venue":"arXiv (Cornell University)","topic":"Advanced Mathematical Identities","field":"Mathematics","cited_by":3,"is_retracted":false,"has_abstract":true,"ca_institutions":"","funders":"Hausdorff Research Institute for Mathematics; Banff International Research Station for Mathematical Innovation and Discovery; Uppsala Universitet; Kavli Institute for Theoretical Physics, University of California, Santa Barbara; National Science Foundation","keywords":"Genus; Riemann surface; Riemann hypothesis; Mathematics; Pure mathematics; Botany; Biology","routes":{"ca_aff":false,"ca_fund":true,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":true},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0009729851,0.0007698187,0.0006158982,0.002890245,0.002177893,0.002583676,0.0009996945,0.0009750462,0.003995829],"category_scores_gemma":[0.00287561,0.0003466215,0.0009765849,0.0009673402,0.003107436,0.00508553,0.00247535,0.002879013,0.0008014433],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001554089,"about_ca_system_score_gemma":0.0005947092,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.000896051,"about_ca_topic_score_gemma":0.0006895849,"domain_scores_codex":[0.9992478,0.000120064,0.00005398068,0.0001250001,0.0002959225,0.000157288],"domain_scores_gemma":[0.9989247,0.0002507826,0.0001785074,0.000204794,0.000200328,0.00024096],"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":[0.000009794125,0.00001609199,0.0003142475,0.00001802041,0.000002423813,0.0001331148,0.000293109,0.0006702431,0.001487627,0.994444,0.0002326415,0.002378694],"study_design_scores_gemma":[0.000007688789,0.00001961515,0.000800622,0.00002002836,0.000004813201,0.0002644091,0.000166286,0.009814911,0.001841317,0.9841136,0.002928089,0.00001863995],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.7132295,0.0008398103,0.204869,0.001030215,0.0003591079,0.00008432379,0.0001989651,0.0003322612,0.07905671],"genre_scores_gemma":[0.9628157,0.0003995169,0.02140166,0.0001867968,0.00018189,0.00006292957,0.0001266964,0.0001285676,0.01469624],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.003995829,"threshold_uncertainty_score":0.01336741,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1798575986515684,"score_gpt":0.2638705058641389,"score_spread":0.08401290721257054,"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."}}