{"paper":{"title":"Pants Decomposition of the Punctured Plane","arxiv_id":"cs/0602080","primary_cat":"cs.CG","submitted_at":"2006-02-22T19:08:48+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. 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":false,"role":"background","text":"A pants decomposition of an orientable surface S is a collection of simple cycles that partition S into pants, i.e., surfaces of genus zero with three boundary cycles.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.06,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.37,"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":0.87,"id":"s1","own":false,"role":"background","text":"Given a set P of n points in the plane, we consider the problem of computing a pants decomposition of the surface S which is the plane minus P, of minimum total length.","hedge":{"p":0.8,"label":"asserted"},"own_p":0.22,"main_claim_p":0.08,"quantitative":true,"quantitative_p":0.5,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.0,"background":0.87,"limitation":0.0,"future_work":0.0,"contribution":0.13,"interpretation":0.0}},{"i":2,"p":0.75,"id":"s2","own":true,"role":"contribution","text":"We give a polynomial-time approximation scheme using Mitchell's guillotine rectilinear subdivisions.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.31,"quantitative":false,"quantitative_p":0.26,"role_probabilities":{"gap":0.0,"method":0.22,"result":0.03,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.75,"interpretation":0.0}},{"i":3,"p":0.9,"id":"s3","own":true,"role":"contribution","text":"We give a quartic-time algorithm to compute the shortest pants decomposition of S when the cycles are restricted to be axis-aligned boxes, and a quadratic-time algorithm when all the points lie on a line; both exact algorithms use dynamic programming with Yao's speedup.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.95,"main_claim_p":0.18,"quantitative":true,"quantitative_p":0.96,"role_probabilities":{"gap":0.0,"method":0.03,"result":0.07,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.9,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.88,"text":"We give a polynomial-time approximation scheme using Mitchell's guillotine rectilinear subdivisions.","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":3661,"cost_usd_reported":0.000154},"compiled_at":"2026-09-23","bank_version":"abstract-p1-20260923","model_version":"classifier-1.13-20260917","abstract_states":{"claims_first":0.04,"states_limitation":0.46,"human_participants":0.01,"controlled_comparison":0.02,"randomized_assignment":0.01,"states_quantitative_result":0.86,"compares_with_prior_results":0.09,"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":0.96,"value":"method or tool","probabilities":{"review":0.0,"method_or_tool":0.96,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.04,"dataset_or_benchmark":0.0,"position_or_commentary":0.0}},"contribution_statement":{"p":0.7,"text":"We give a polynomial-time approximation scheme using Mitchell's guillotine rectilinear subdivisions.","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 v1"],"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}}