{"id":"d162e18d-25a9-4411-aa6f-03a9c866dd23","arxiv_id":"1908.00450","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":0,"one_line_summary":"The paper claims an optimal endpoint-corrected trapezoidal rule in the Sobolev space W_2^{(2,1)} with an O(h^4) error, but the proof of the error formula is algebraically inconsistent.","lead":"This paper derives an optimal numerical integration rule for functions with limited smoothness by adding endpoint derivative corrections to the trapezoidal rule. It claims the error is O(h^4) and smaller than the Euler-Maclaurin rule, but the proof contains algebraic errors that break the derivation.","discovery_kind":"extension","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-14T16:00:39.794752+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}