Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture
openconfidence 70%
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Precise statement
Does the Dinitz-Garg-Goemans cost-preserving unsplittable-flow rounding conjecture survive on acyclic planar instances with only four terminals? An explicit instance answers no: every cost-nonincreasing unsplittable routing has upper overload at least $335$ while the maximum demand is $294$.
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fidelity, correctness, priority, or novelty.
What AI did
GPT-5.6 Pro
GPT-5.6 Pro carried out much of the construction search, symbolic derivation, proof development, exact-verifier development, adversarial critique and manuscript preparation. The human author selected and framed the problem, directed the investigation, caught a cost-normalization error, required exact and adversarial checks, set the claim scope and approved the release. A later Codex session independently re-encoded the key graph, finite and symbolic checks and ran deterministic stress and release checks.
The immutable v0.1.0 public disclosure ships a manuscript, exact data, an exhaustive verifier over all 16 routings and all 13 arcs, mutation tests, deterministic hashes and a separate AI-assisted computational cross-check. The attained certificate is $335/294$; the package also proves the limiting lower bound $(299 - 41sqrt{41})/32$, with sharpness only in the stated fixed-topology, equal-full-cost, two-cheap-choice model. Released 2026-07-23, one day after the first public disproof of the general conjecture, and developed independently of it.