{"paper":{"title":"On the G\\\"ottsche Threshold","arxiv_id":"1204.6254","primary_cat":"math.AG","submitted_at":"2012-04-27T15:45:56+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 a line bundle L on a smooth surface S, it is now known that the degree of the Severi variety of cogenus-d curves is given by a universal polynomial in the Chern classes of L and S if L is d-very ample.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.07,"main_claim_p":0.17,"quantitative":false,"quantitative_p":0.14,"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":0.63,"id":"s1","own":true,"role":"result","text":"For S rational, we relax the latter condition substantially: it suffices that three key loci be of codimension more than d.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.85,"main_claim_p":0.37,"quantitative":true,"quantitative_p":0.86,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.63,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.37,"interpretation":0.0}},{"i":2,"p":0.94,"id":"s2","own":true,"role":"result","text":"As corollaries, we prove that the condition conjectured by G\\\"ottsche suffices if S is P^2 or S is any Hirzebruch surface, and that a similar condition suffices if S is any classical del Pezzo surface.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.45,"quantitative":false,"quantitative_p":0.18,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.94,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.02}}]},"compiled":{"main_claim":{"p":0.88,"text":"For S rational, we relax the latter condition substantially: it suffices that three key loci be of codimension more than d.","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":3058,"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":0.05,"states_limitation":0.54,"human_participants":0.01,"controlled_comparison":0.03,"randomized_assignment":0.01,"states_quantitative_result":0.23,"compares_with_prior_results":0.79,"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":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":0.95,"text":"For S rational, we relax the latter condition substantially: it suffices that three key loci be of codimension more than d.","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}}