{"paper":{"title":"Characteristic numbers of elliptic fibrations with non-trivial Mordell-Weil groups","arxiv_id":"1808.07054","primary_cat":"hep-th","submitted_at":"2018-08-21T18:00:00+00:00","version_compiled":"v1"},"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 v1","sentences":[{"i":0,"p":1.0,"id":"s0","own":true,"role":"contribution","text":"We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.96,"main_claim_p":0.3,"quantitative":false,"quantitative_p":0.04,"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":0.63,"id":"s1","own":true,"role":"contribution","text":"We first consider the models of type E$_{9-d}$ with $d=1,2,3,4$ whose generic fibers are normal elliptic curves of degree $d$.","hedge":{"p":0.93,"label":"asserted"},"own_p":0.7,"main_claim_p":0.04,"quantitative":true,"quantitative_p":0.85,"role_probabilities":{"gap":0.0,"method":0.37,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.63,"interpretation":0.0}},{"i":2,"p":0.91,"id":"s2","own":true,"role":"contribution","text":"We then analyze the characteristic numbers of the $Q_7$-model, which provides a smooth model for elliptic fibrations of rank one and generalizes the E$_5$, E$_6$, and E$_7$-models.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.88,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.47,"role_probabilities":{"gap":0.0,"method":0.09,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.91,"interpretation":0.0}},{"i":3,"p":0.99,"id":"s3","own":true,"role":"contribution","text":"Finally, we examine the characteristic numbers of $G$-models with $G=\\text{SO}(n)$ with $n=3,4,5,6$ and $G=\\text{PSU}(3)$ whose Mordell-Weil groups are respectively $\\mathbb{Z}/2\\mathbb{Z}$ and $\\mathbb{Z}/3 \\mathbb{Z}$.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.92,"main_claim_p":0.06,"quantitative":true,"quantitative_p":0.75,"role_probabilities":{"gap":0.0,"method":0.01,"result":0.0,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.99,"interpretation":0.0}},{"i":4,"p":0.48,"id":"s4","own":true,"role":"contribution","text":"In each case, we compute the Chern and Pontryagin numbers, the Euler characteristic, the holomorphic genera, the Todd-genus, the L-genus, the A-genus, and the eight-form curvature invariant from M-theory.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.21,"quantitative":false,"quantitative_p":0.3,"role_probabilities":{"gap":0.0,"method":0.36,"result":0.16,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.48,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.57,"text":"We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups.","location":"abstract s0","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":4580,"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":0.06,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.1,"compares_with_prior_results":0.11,"mentions_code_or_data_availability":0.02},"evidential_basis":{"p":0.85,"value":"proof or derivation","probabilities":{"argument":0.0,"literature":0.0,"proof_or_derivation":0.85,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.15}},"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":0.9,"text":"We compute characteristic numbers of elliptically fibered fourfolds with multisections or non-trivial Mordell-Weil groups.","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 v1"],"levels_not_run":["S sections","T body sentences","C citations","R cross-paper relations"],"sentences_examined":5,"sentences_in_abstract":5},"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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