cd /news/artificial-intelligence/gpt-5-6-pro-finds-counterexample-to-… · home › topics › artificial-intelligence › article
[ARTICLE · art-69622] src=xcancel.com ↗ pub= topic=artificial-intelligence verified=true sentiment=↑ positive

GPT 5.6 Pro finds counterexample to Dinitz-Garg-Goemans conjecture

GPT 5.6 Pro has found a counterexample to the Dinitz-Garg-Goemans conjecture, a graph theory problem open for approximately 30 years. The graph exhibits a fractional flow cost of 58, while any unsplittable flow with capacity violation ≤15 has cost at least 60, disproving the conjecture. The user who discovered the counterexample stated they spent many weeks thinking about the problem.

read1 min views1 publishedJul 23, 2026
GPT 5.6 Pro finds counterexample to Dinitz-Garg-Goemans conjecture
Image: Xcancel (auto-discovered)

Dinitz-Garg-Goemans conjecture is false. This graph theory problem was open for ~30 years. The graph below has fractional flow cost 58. Any unsplittable flow (with capacity violation <=15) has cost at least 60. Chat with GPT 5.6 Pro where this was found:

chatgpt.com/share/6a60b2eb-0…Jul 22, 2026 · 12:18 PM UTC 186

662

7,566

2,566,273

I know counterexamples to old conjectures are becoming a meme at this point. But I really cared about this problem and spent many weeks thinking about it a while ago (in both directions, proof and disproof). I think almost all graph flows experts thought about this problem.

12

11

1,536

107,200

source & further reading
xcancel.com — original article The 20x plan is now the 10x plan, and the 5x plan is the 2.5x plan Extra hidden computations in LLM using dot tokens for multi-hop reasoning GPT-5.6-Sol just accidentally deleted almost ALL of my Mac's files
── more in #artificial-intelligence 4 stories · sorted by recency
── more on @gpt 5.6 pro 3 stories trending now
sponsored brought to you by zahid.host 4,200+ EU-deployed projects
reading about agents? ship yours in a single git push.

Run your AI side-project on zahid.host

EU-based hosting, git-push deploys, automatic HTTPS, no cold starts. Free tier with a custom domain — perfect for shipping the agent you just read about.

$git push zahid main
→ Live at https://your-agent.zahid.host ✓
Get free account → Pricing
from €0/mo · no card required
LIVE [news/gpt-5-6-pro-finds-co…] indexed:0 read:1min 2026-07-23 · —