Selected research history · publication v4
Follow the ideas, results and limitations over time. This is a selected history, not a complete literature survey or a measure of how close the problem is to being solved.
Current state & remaining question →Viewing the timeline from pinned publication v4.
5 selected milestones · Source coverage checked 2026-10-13 · Historical annotation and mathematical review remain separate.
Dinitz, Garg and Goemans establish additive congestion bounded by the largest demand.
Scope & review: The folklore cost strengthening is a separate assertion, later stated as Conjecture 1.3 in the 2023 paper.
Historical annotation review: pending. The date refers to the publication, with the precision supported by the source.
Traub, Vargas Koch and Zenklusen prove the cost guarantee with two-sided deviation at most twice the largest demand.
Scope & review: The larger allowance is essential to distinguishing this theorem from the refuted question.
Historical annotation review: pending. The date refers to the preprint, with the precision supported by the source.
The verification projects attribute the discovery to Dmitry Rybin’s GPT-5.6 Pro session.
Scope & review: The original discovery and subsequent formal checks are separate contributions.
Historical annotation review: pending. The date refers to the announcement, with the precision supported by the source.
Formalization
Ramos, Hulak and de Queiroz supply the generic flow model and exhaustive finite argument.
Scope & review: The AFP entry date is distinct from the generated document’s August revision date.
Historical annotation review: pending. The date refers to the formalization, with the precision supported by the source.
Formalization
Jason Hickey’s project checks the exact optimum and the literature-faithful conjecture refutation.
Scope & review: This is a source-reported verification, not an OpenMath build.
Historical annotation review: pending. The date refers to the formalization, with the precision supported by the source.