{"id":"5e7efda6-0c32-41b1-811f-b336ad9abbf3","arxiv_id":"1908.00406","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"A new invariant from cycle maps on curves shows that a smooth threefold intersection of two quadrics over a subfield of C is rational if and only if it contains a line over that field.","lead":"Algebraic threefolds cut out by two quadratic equations in five-dimensional projective space are rational over a field exactly when they contain a straight line defined over that field. The paper introduces new birational obstructions built from cycle class maps of curves, then applies them to this classical family.","discovery_kind":"new_method","skeptic_critique":null,"referee_report":null,"author_rebuttal":null,"desk_editor":null,"rs_alignment":null,"lean_confirmation":null,"pith_extraction":null,"created_at":"2026-08-14T15:59:27.648420+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":null,"supporting_citations":[],"review_version":1}