{"paper":{"title":"Is there a topological Bogomolov--Miyaoka--Yau inequality?","arxiv_id":"math/0602562","primary_cat":"math.AG","submitted_at":"2006-02-24T22:14:02+00:00","version_compiled":"v2"},"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 v2","sentences":[{"i":0,"p":0.76,"id":"s0","own":false,"role":"contribution","text":"The aim of this paper is to consider a possible extension of the Bogomolov--Miyaoka--Yau inequality to differentiable orbifolds.","hedge":{"p":0.63,"label":"hedged_possibility"},"own_p":0.39,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.0,"background":0.21,"limitation":0.0,"future_work":0.02,"contribution":0.76,"interpretation":0.0}},{"i":1,"p":0.76,"id":"s1","own":false,"role":"background","text":"The conjectured extension is related to the Montgomery--Yang problem about circle actions on the 5--sphere and also to the H--cobordism of Seifert fibered 3--manifolds.","hedge":{"p":0.71,"label":"asserted"},"own_p":0.14,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.76,"limitation":0.0,"future_work":0.0,"contribution":0.14,"interpretation":0.1}},{"i":2,"p":0.75,"id":"s2","own":true,"role":"contribution","text":"Related conjectures on algebraic surfaces with quotient singularities which have the same rational homology as the projective plane are also considered.","hedge":{"p":0.8,"label":"asserted"},"own_p":0.51,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.14,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.25,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.0}},{"i":3,"p":0.65,"id":"s3","own":true,"role":"result","text":"Finally we give such examples which are birational to the projective plane yet have ample canonical class.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.35,"quantitative":false,"quantitative_p":0.06,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.65,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.35,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.98,"text":"Finally we give such examples which are birational to the projective plane yet have ample canonical class.","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":3637,"cost_usd_reported":0.0},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13.0","abstract_states":{"claims_first":0.05,"states_limitation":0.17,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.06,"compares_with_prior_results":0.18,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":0.55,"value":"proof or derivation","probabilities":{"argument":0.43,"literature":0.02,"proof_or_derivation":0.55,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.51,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.51,"dataset_or_benchmark":0.0,"position_or_commentary":0.49}},"contribution_statement":{"p":0.97,"text":"Finally we give such examples which are birational to the projective plane yet have ample canonical class.","location":"abstract s3"}},"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 v2"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":4,"sentences_in_abstract":4},"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}}