{"paper":{"title":"Higher minors and Van Kampen's obstruction","arxiv_id":"math/0602531","primary_cat":"math.CO","submitted_at":"2006-02-23T13:19:19+00:00","version_compiled":"v3"},"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 v3","sentences":[{"i":0,"p":1.0,"id":"s0","own":true,"role":"contribution","text":"We generalize the notion of graph minors to all (finite) simplicial complexes.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.94,"main_claim_p":0.06,"quantitative":false,"quantitative_p":0.1,"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":0.97,"id":"s1","own":true,"role":"result","text":"For every two simplicial complexes H and K and every nonnegative integer m, we prove that if H is a minor of K then the non vanishing of Van Kampen's obstruction in dimension m (a characteristic class indicating non embeddability in the (m-1)-sphere) for H implies its non vanishing for K.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.94,"main_claim_p":0.69,"quantitative":false,"quantitative_p":0.37,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.97,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.03,"interpretation":0.0}},{"i":2,"p":0.79,"id":"s2","own":true,"role":"result","text":"As a corollary, based on results by Van Kampen and Flores, if K has the d-skeleton of the (2d+2)-simplex as a minor, then K is not embeddable in the 2d-sphere.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.53,"main_claim_p":0.25,"quantitative":true,"quantitative_p":0.94,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.79,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.0,"interpretation":0.21}},{"i":3,"p":0.83,"id":"s3","own":true,"role":"result","text":"We answer affirmatively a problem asked by Dey et. al. concerning topology-preserving edge contractions, and conclude from it the validity of the generalized lower bound inequalities for a special class of triangulated spheres.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.91,"main_claim_p":0.13,"quantitative":false,"quantitative_p":0.4,"role_probabilities":{"gap":0.0,"method":0.0,"result":0.83,"background":0.0,"limitation":0.0,"future_work":0.0,"contribution":0.17,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.96,"text":"For every two simplicial complexes H and K and every nonnegative integer m, we prove that if H is a minor of K then the non vanishing of Van Kampen's obstruction in dimension m (a characteristic class indicating non embeddability in the (m-1)-sphere) for H implies its non vanishing for K.","location":"abstract s1","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":3813,"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":0.06,"states_limitation":0.14,"human_participants":0.01,"controlled_comparison":0.01,"randomized_assignment":0.01,"states_quantitative_result":0.53,"compares_with_prior_results":0.62,"mentions_code_or_data_availability":0.01},"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":0.8,"text":"We generalize the notion of graph minors to all (finite) simplicial complexes.","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 v3"],"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}}