{"paper":{"title":"The chi-y genera of relative Hilbert schemes for linear systems on Abelian and K3 surfaces","arxiv_id":"1307.4316","primary_cat":"math.AG","submitted_at":"2013-07-16T15:57:17+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-1.13-20260917 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":1.0,"id":"s0","own":false,"role":"background","text":"For an ample line bundle on an Abelian or K3 surface, minimal with respect to the polarization, the relative Hilbert scheme of points on the complete linear system is known to be smooth.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.04,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":1.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":1,"p":0.6,"id":"s1","own":true,"role":"contribution","text":"We give an explicit expression in quasi-Jacobi forms for the chi-y genus of the restriction of the Hilbert scheme to a general linear subsystem.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.81,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.4,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.6,"interpretation":0.0}},{"i":2,"p":0.67,"id":"s2","own":false,"role":"interpretation","text":"This generalizes a result of Yoshioka and Kawai for the complete linear system on the K3 surface, a result of Maulik, Pandharipande, and Thomas on the Euler characteristics of linear subsystems on the K3 surface, and a conjecture of the authors.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.45,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.08,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.08,"background":0.04,"limitation":0.0,"future_work":0.0,"contribution":0.2,"interpretation":0.67}}]},"compiled":{"main_claim":{"p":1.0,"text":"We give an explicit expression in quasi-Jacobi forms for the chi-y genus of the restriction of the Hilbert scheme to a general linear subsystem.","location":"abstract s1","hedge_strength":{"p":1.0,"label":"asserted"}},"provenance":{"route":{"via":"OpenRouter","model":"classifier-1.13","endpoint":"https://openrouter.ai/api/v1/systemone","provider":"TypeSafe"},"packing":"one request per paper","requests":1,"input_tokens":3049,"cost_usd_reported":0.000128},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.07,"states_limitation":0.18,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.14,"compares_with_prior_results":0.95,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.99,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.01,"proof_or_derivation":0.99,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":1.0,"value":"theoretical result","probabilities":{"review":0.0,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":1.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":1.0,"text":"We give an explicit expression in quasi-Jacobi forms for the chi-y genus of the restriction of the Hilbert scheme to a general linear subsystem.","location":"abstract s1"}},"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":3,"sentences_in_abstract":3},"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}}