Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture

restricted planar four-terminal case

Exact FrontierDelta

Prior state unknown→disproved

Scope and record

Occurred: Jul 23, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.

Canonical aliases: Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture · Four-terminal planar DGG

Confidence: Not scored

Registry verification: unreviewed · preprint · variant

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Attribution

VibeMathed
registry · event recorded by

Matthew Protti
human · human collaborator

GPT-5.6 Pro
model · ai model contributor · OpenAI

Evidence vector

SourceReplayReproducedFormal proofStatement auditExternal checkExpert reviewPeer review

Named evidence

VibeMathed record: Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture

specialist registry · passed

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.

Source ↗

Four-Terminal Planar Case of the Dinitz-Garg-Goemans Cost Conjecture

preprint · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

Source ↗

Manuscript (PDF)

paper · pending

paper link supplied by the VibeMathed registry.

Source ↗

Exact verification suite (verify_all.py)

code · pending

code link supplied by the VibeMathed registry.