{"paper":{"title":"Euler systems for self-dual Hecke characters over biquadratic fields with applications","arxiv_id":"2610.28196","primary_cat":"math.NT","submitted_at":"2026-10-20T13:36:43+00:00","version_compiled":"v1"},"notice":"Every quoted sentence is the authors' text from the arXiv listing abstract. Labels and probabilities are the outputs of classifier-1.13.0 on the question bank abstract-p1-20260923, exactly as returned. No sentence in this record was written by a language model.","schema":"pith.compiled-record/v0","status":"compiled","abstract":{"source":"arXiv listing abstract v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":true,"role":"contribution","text":"We construct a new Euler system attached to a self-dual Hecke character $\\chi$ over an imaginary biquadratic field $K_0$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.97,"main_claim_p":0.26,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":1.0,"interpretation":0.0}},{"i":1,"p":0.73,"id":"s1","own":true,"role":"contribution","text":"The Euler system is anticyclotomic in the sense of Jetchev--Nekov\\'a{\\v r}--Skinner.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.61,"main_claim_p":0.07,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.1,"result":0.1,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.73,"interpretation":0.07}},{"i":2,"p":0.96,"id":"s2","own":true,"role":"result","text":"As arithmetic applications, we deduce instances of the Bloch--Kato conjecture in analytic ranks $0$, $1$, and $2$ (the last one for certain CM abelian surfaces).","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.27,"quantitative":true,"quantitative_p":0.94,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.96,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.0}},{"i":3,"p":0.91,"id":"s3","own":true,"role":"result","text":"In addition, we establish the full Iwasawa--Greenberg main conjecture for $\\chi$ over $K_0$.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.33,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.91,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.0}},{"i":4,"p":0.64,"id":"s4","own":true,"role":"interpretation","text":"In this biquadratic setting, our work generalizes Rubin's work on the Iwasawa main conjectures for imaginary quadratic fields using Euler systems of elliptic units, while complementing known results of Hida and Hsieh for general CM fields.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.69,"main_claim_p":0.08,"quantitative":false,"quantitative_p":0.4,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.24,"limitation":0.0,"future_work":0.0,"contribution":0.12,"interpretation":0.64}}]},"compiled":{"main_claim":{"p":0.64,"text":"In addition, we establish the full Iwasawa--Greenberg main conjecture for $\\chi$ over $K_0$.","location":"abstract s3","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"TypeSafe API","model":"classifier-1.13.0","endpoint":"https://api.typesafe.ai/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":4374,"cost_usd_reported":0.0},"compiled_at":"2026-10-21","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.08,"states_limitation":0.33,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.49,"compares_with_prior_results":0.96,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":1.0,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":1.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.96,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.04,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.96,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":1.0,"text":"We construct a new Euler system attached to a self-dual Hecke character $\\chi$ over an imaginary biquadratic field $K_0$.","location":"abstract s0"}},"coverage":{"tier":"abstract","levels_run":["P abstract"],"not_examined":["full text","figures and tables","references and citing sentences","relations to other papers"],"sources_read":["arXiv listing abstract v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":5,"sentences_in_abstract":5},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; the figure is how often the published label matches their consensus","sentence_role_agreement":0.92,"main_claim_agreement":0.908,"typed_citation_agreement":0.933,"typed_citation_agreement_95_interval":[0.917,0.945],"review_comments_accurate":0.758,"review_comments_accurate_95_interval":[0.684,0.82],"review_caught_admitted_error_found_or_related":0.448}}