{"paper":{"title":"The Plateau problem for polygonal boundary curves in Minkowski 3-space","arxiv_id":"1012.3582","primary_cat":"math.DG","submitted_at":"2010-12-16T12:46:03+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-1.13-20260917 on the question bank abstract-p1-20260923, exactly as returned. 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Umehara and K. Yamada.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.24,"main_claim_p":0.05,"quantitative":false,"quantitative_p":0.07,"role_probabilities":{"gap":0.01,"method":0.52,"result":0.0,"background":0.11,"limitation":0.3,"future_work":0.0,"contribution":0.05,"interpretation":0.01}},{"i":4,"p":0.98,"id":"s4","own":true,"role":"result","text":"We prove that any given spacelike polygonal curve in generic position in Minkowski 3-space bounds at least one maxface of disk-type.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.9,"quantitative":true,"quantitative_p":0.63,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.98,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.02,"interpretation":0.0}},{"i":5,"p":0.87,"id":"s5","own":false,"role":"gap","text":"This is a new result, since the only known result for the Plateau problem in Minkowski space (due to N.","hedge":{"p":0.98,"label":"asserted"},"own_p":0.32,"main_claim_p":0.09,"quantitative":true,"quantitative_p":0.53,"role_probabilities":{"gap":0.87,"method":0.0,"result":0.01,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.09,"interpretation":0.02}},{"i":6,"p":0.75,"id":"s6","own":false,"role":"gap","text":"Quien) deals with boundary curves of regularity $C^{3,\\alpha}$.","hedge":{"p":0.95,"label":"asserted"},"own_p":0.05,"main_claim_p":0.02,"quantitative":false,"quantitative_p":0.2,"role_probabilities":{"gap":0.75,"method":0.0,"result":0.0,"background":0.24,"limitation":0.0,"future_work":0.0,"contribution":0.01,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":1.0,"text":"We prove that any given spacelike polygonal curve in generic position in Minkowski 3-space bounds at least one maxface of disk-type.","location":"abstract s4","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":5507,"cost_usd_reported":0.000231},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.68,"states_limitation":0.72,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.13,"compares_with_prior_results":0.95,"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":0.98,"text":"We prove that any given spacelike polygonal curve in generic position in Minkowski 3-space bounds at least one maxface of disk-type.","location":"abstract s4"}},"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":7,"sentences_in_abstract":7},"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}}