{"payload":{"schema_version":"research-record-v0","publication":{"version":5,"sha256":"fa3ec89969ca35296d8a729b4db53d78544586f1431dedded1cc72e570218ef2","published_at":"2026-10-13T14:24:25.018152+00:00","reason":"Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.","withdrawn":false,"draft":{"representations":[{"schema_version":"visual-representation-v1","id":"dinitz-garg-goemans-flow-setup","version":5,"subject":{"kind":"problem","id":"problem-dinitz-garg-goemans-flow","sha256":"002cb60f020e0326c4fb388ec2d65d70c184abe6a768df926d7421c9edb30926"},"purpose":"setup","title":"The seven-node cost counterexample","caption":"Arrow labels give fractional load / cost per unit. Terminal demands are t1: 15, t2: 10 and t3: 15; d_max = 15. Every arc capacity equals its fractional load.","description":"Terminal demands are t1: 15, t2: 10 and t3: 15. 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Labels are load / unit cost; the full text view lists every arc."}}],"visuals":[{"representation":{"id":"dinitz-garg-goemans-flow-setup","version":5},"section":"question"}],"claim_relations":[{"claim":{"id":"claim-flow-cost-preserving-rounding","version":2},"relation":"primary_formulation","relationship_note":"Goemans’ cost-enhanced assertion is refuted; the original congestion-only theorem is not.","result":"refuted","report_ids":["dinitz-garg-goemans-flow:report:refutation:v2"],"independent_review":"pending"},{"claim":{"id":"claim-flow-seven-vertex-counterexample","version":2},"relation":"counterexample","relationship_note":"A finite exhaustive path-choice witness. 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proof text is not republished.","check_interval_days":90}],"entries":[{"id":"dinitz-garg-goemans-flow:entry:literature:v1","source_version_id":"dinitz-garg-goemans-flow:source:literature:v1","item_id":"literature","url":"https://arxiv.org/abs/2308.02651v1","wording":"The paper states the original congestion theorem, Goemans’ cost-enhanced conjecture and a planar theorem with twice the largest-demand allowance.","wording_kind":"paraphrase","locator":"Definition 1.1, Theorem 1.2, Conjecture 1.3 and Theorem 1.8","supersedes":null},{"id":"dinitz-garg-goemans-flow:entry:isabelle:v2","source_version_id":"dinitz-garg-goemans-flow:source:isabelle:v2","item_id":"isabelle","url":"https://isa-afp.org/entries/Dinitz_Garg_Goemans_Counterexample.html","wording":"A directed seven-vertex, nine-arc instance has fractional cost 58 and no congestion-allowed unsplittable routing of cost below 60.","wording_kind":"paraphrase","locator":"Generic path-flow model; directed graph realization; bounded_unsplittable_cost and dinitz_garg_goemans_cost_counterexample","supersedes":"dinitz-garg-goemans-flow:entry:isabelle:v1"},{"id":"dinitz-garg-goemans-flow:entry:lean:v2","source_version_id":"dinitz-garg-goemans-flow:source:lean:v2","item_id":"lean","url":"https://github.com/jyh/dinitz-verify/tree/ffba3523f0edd14be3460d039f22a6b98c02fd9e","wording":"The project verifies the rational and real cost conjecture refutations and exact optimum 60 for the displayed instance.","wording_kind":"paraphrase","locator":"Submission.lean headline theorems; 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exact congestion-constrained optimum 60.","source_date":"2026-08-01","observed_on":"2026-10-13","evidence_url":"https://github.com/jyh/dinitz-verify/tree/ffba3523f0edd14be3460d039f22a6b98c02fd9e","supersedes":"dinitz-garg-goemans-flow:report:lean:v1"},{"id":"dinitz-garg-goemans-flow:report:congestion:v1","entry_id":"dinitz-garg-goemans-flow:entry:literature:v1","state":"resolved","source_label":"Original congestion-only theorem","scope":"No cost-preservation assertion.","source_date":"2023-08-04","observed_on":"2026-10-13","evidence_url":"https://arxiv.org/abs/2308.02651v1","supersedes":null},{"id":"dinitz-garg-goemans-flow:report:planar:v1","entry_id":"dinitz-garg-goemans-flow:entry:literature:v1","state":"resolved","source_label":"Planar cost theorem with doubled allowance","scope":"Planar instances with upper and lower deviation at most 2 d_max.","source_date":"2023-08-04","observed_on":"2026-10-13","evidence_url":"https://arxiv.org/abs/2308.02651v1","supersedes":null}]},"status":{"state":"refuted","label":"Resolved · counterexample","extent":"full_statement","summary":"The exact-cost strengthening is refuted by a finite witness in the cited Isabelle and Lean sources. 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