Publication v8
Original question, distinct results, proof provenance, selected history and an explanatory schematic.
Formal proofs: Pinned Isabelle/HOL and Lean sources report complete finite-witness checks. They have separate theorem targets and provenance. No OpenMath execution of either project is recorded.
AI-assisted work: Dmitry Rybin and his GPT-5.6 Pro session receive discovery credit, as reported by the verification sources. Arthur Freitas Ramos, David Barros Hulak and Ruy Jose Guerra Barretto de Queiroz authored the Isabelle verification. Jason Hickey, with Claude, authored the separate Lean verification. Dinitz, Garg and Goemans proved the older congestion theorem; Traub, Vargas Koch and Zenklusen supplied the later precise cost formulation and planar theorem.
Selected primary papers, exact formal declarations, project provenance and official descriptions checked on 13 October 2026.
Checked Oct 13, 2026 · independent review pending.
Cost-preserving rounding conjecture refuted · observed Oct 13, 2026
Source status dated Jul 22, 2026 · observed Oct 13, 2026
The conjunction of a largest-demand congestion allowance and preservation of fractional cost.
Vera Traub, Laura Vargas Koch, Rico Zenklusen · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
dinitz-garg-goemans-flow:entry:literature:v1Arthur Freitas Ramos, David Barros Hulak, Ruy Jose Guerra Barretto de Queiroz · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
dinitz-garg-goemans-flow:entry:isabelle:v2Jason Hickey · metadata-link · Original source license and document rights apply.
OpenMath supplies its own mathematical paraphrases and links; proof text is not republished. Rights / source terms
dinitz-garg-goemans-flow:entry:lean:v2Source-linked pilot import; independent mathematical review remains pending.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.