{"paper":{"title":"The relative Riemann-Roch theorem from Hochschild homology","arxiv_id":"math/0603127","primary_cat":"math.AG","submitted_at":"2006-03-06T04:02:37+00:00","version_compiled":"v5"},"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 v5","sentences":[{"i":0,"p":0.69,"id":"s0","own":true,"role":"contribution","text":"This write up attempts to clarify a preprint by Markarian [2] which proves This paper attempts to clarify a preprint of Markarian [2].","hedge":{"p":0.58,"label":"asserted"},"own_p":0.57,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.17,"role_probabilities":{"gap":0.01,"method":0.0,"result":0.0,"background":0.3,"limitation":0.0,"future_work":0.0,"contribution":0.69,"interpretation":0.0}},{"i":1,"p":0.79,"id":"s1","own":false,"role":"background","text":"The preprint by Markarian [2] proves the relative Riemann-Roch theorem using a result describing how the HKR map fails to respect comultiplication.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.27,"quantitative":false,"quantitative_p":0.09,"role_probabilities":{"gap":0.0,"method":0.08,"result":0.07,"background":0.79,"limitation":0.0,"future_work":0.0,"contribution":0.06,"interpretation":0.0}},{"i":2,"p":0.96,"id":"s2","own":true,"role":"contribution","text":"This paper elaborates on the core computations in [2].","hedge":{"p":0.98,"label":"asserted"},"own_p":0.74,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.0,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.96,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":false,"role":"result","text":"These computations show that the HKR map twisted by the square root of the Todd genus \"almost preserves\" the Mukai pairing.","hedge":{"p":0.97,"label":"asserted"},"own_p":0.44,"main_claim_p":0.32,"quantitative":false,"quantitative_p":0.34,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.99,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.01}},{"i":4,"p":0.79,"id":"s4","own":false,"role":"interpretation","text":"This settles a part of a conjecture of Caldararu[3].","hedge":{"p":1.0,"label":"asserted"},"own_p":0.45,"main_claim_p":0.2,"quantitative":false,"quantitative_p":0.05,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.19,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.79}},{"i":5,"p":0.58,"id":"s5","own":false,"role":"result","text":"The relative Riemann-Roch theorem follows from this and a result of Caldararu[4].","hedge":{"p":1.0,"label":"asserted"},"own_p":0.28,"main_claim_p":0.37,"quantitative":false,"quantitative_p":0.04,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.58,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.39}}]},"compiled":{"main_claim":{"p":0.75,"text":"The relative Riemann-Roch theorem follows from this and a result of Caldararu[4].","location":"abstract s5","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":4806,"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":0.04,"states_limitation":0.26,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.05,"compares_with_prior_results":0.7,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.95,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.04,"proof_or_derivation":0.95,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.01}},"contribution_type":{"p":0.64,"value":"theoretical result","probabilities":{"review":0.11,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.64,"dataset_or_benchmark":0.0,"position_or_commentary":0.25}},"contribution_statement":{"p":0.78,"text":"This paper elaborates on the core computations in [2].","location":"abstract s2"}},"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 v5"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":6,"sentences_in_abstract":6},"measured_accuracy":{"url":"https://pith.science/accuracy","measured_on":"2026-10-02","method":"two independent model families labelled a fresh random sample blind; 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