{"paper":{"title":"Second variation of Zhang's lambda-invariant on the moduli space of curves","arxiv_id":"1002.1618","primary_cat":"math.AG","submitted_at":"2010-02-08T15:00:06+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":true,"role":"contribution","text":"We compute the second variation of the \\lambda-invariant, recently introduced by S.","hedge":{"p":0.96,"label":"asserted"},"own_p":0.91,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.32,"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":0.5,"id":"s1","own":false,"role":"contribution","text":"Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi.","hedge":{"p":0.77,"label":"asserted"},"own_p":0.48,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.71,"role_probabilities":{"gap":0.0,"method":0.44,"result":0.0,"background":0.06,"limitation":0.0,"future_work":0.0,"contribution":0.5,"interpretation":0.0}},{"i":2,"p":1.0,"id":"s2","own":true,"role":"result","text":"As a result we prove that (8g+4)\\lambda is equal, up to a constant, to the \\beta-invariant introduced some time ago by R. Hain and D. Reed.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.87,"main_claim_p":0.82,"quantitative":true,"quantitative_p":0.88,"role_probabilities":{"gap":0.0,"method":0.0,"result":1.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.0}},{"i":3,"p":0.92,"id":"s3","own":true,"role":"result","text":"We deduce some consequences; for example we calculate the \\lambda-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.1,"quantitative":false,"quantitative_p":0.1,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.92,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.04,"interpretation":0.04}}]},"compiled":{"main_claim":{"p":1.0,"text":"As a result we prove that (8g+4)\\lambda is equal, up to a constant, to the \\beta-invariant introduced some time ago by R. Hain and D. Reed.","location":"abstract s2","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":3625,"cost_usd_reported":0.000152},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.06,"states_limitation":0.08,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.78,"compares_with_prior_results":0.91,"mentions_code_or_data_availability":0.02},"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":0.88,"text":"We compute the second variation of the \\lambda-invariant, recently introduced by S.","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 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}}