{"paper":{"title":"On the origin of the Korteweg-de Vries equation","arxiv_id":"math/0602661","primary_cat":"math.HO","submitted_at":"2006-02-28T13:02:04+00:00","version_compiled":"v2"},"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 v2","sentences":[{"i":0,"p":1.0,"id":"s0","own":false,"role":"background","text":"The Korteweg-de Vries equation has a central place in a model for waves on shallow water and it is an example of the propagation of weakly dispersive and weakly nonlinear waves.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.05,"main_claim_p":0.04,"quantitative":false,"quantitative_p":0.08,"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":1.0,"id":"s1","own":false,"role":"background","text":"Its history spans a period of about sixty years, starting with experiments of Scott Russell in 1834, followed by theoretical investigations of, among others, Lord Rayleigh and Boussinesq in 1871 and, finally, Korteweg and De Vries in 1895.","hedge":{"p":1.0,"label":"asserted"},"own_p":0.03,"main_claim_p":0.03,"quantitative":true,"quantitative_p":0.95,"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":2,"p":1.0,"id":"s2","own":true,"role":"contribution","text":"In this essay we compare the work of Boussinesq and Korteweg-de Vries, stressing essential differences and some interesting connections.","hedge":{"p":0.91,"label":"asserted"},"own_p":0.72,"main_claim_p":0.09,"quantitative":false,"quantitative_p":0.45,"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":3,"p":0.66,"id":"s3","own":true,"role":"gap","text":"Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.","hedge":{"p":0.99,"label":"asserted"},"own_p":0.57,"main_claim_p":0.12,"quantitative":false,"quantitative_p":0.24,"role_probabilities":{"gap":0.66,"method":0.0,"result":0.01,"background":0.01,"limitation":0.0,"future_work":0.0,"contribution":0.32,"interpretation":0.0}}]},"compiled":{"main_claim":{"p":0.61,"text":"Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.","location":"abstract s3","hedge_strength":{"p":0.99,"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":3735,"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":0.05,"states_limitation":0.13,"human_participants":0.03,"controlled_comparison":0.03,"randomized_assignment":0.01,"states_quantitative_result":0.16,"compares_with_prior_results":0.54,"mentions_code_or_data_availability":0.01},"evidential_basis":{"p":0.97,"value":"literature","probabilities":{"argument":0.03,"literature":0.97,"proof_or_derivation":0.0,"analysis_of_existing_data":0.0,"observation_or_experiment":0.0,"simulation_or_computation":0.0}},"contribution_type":{"p":0.91,"value":"review","probabilities":{"review":0.91,"method_or_tool":0.0,"empirical_study":0.0,"simulation_study":0.0,"theoretical_result":0.0,"dataset_or_benchmark":0.0,"position_or_commentary":0.09}},"contribution_statement":{"p":0.79,"text":"Although there exist a number of articles, reviewing the origin and birth of the Korteweg-de Vries equations, connections and differences, not generally known, are reported.","location":"abstract s3"}},"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 v2"],"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}}