Written on the Wall II, Graph Conjecture 143

Precise statement

For every finite connected graph, is $\operatorname{girth}(G) + 1$ at most the product of its largest induced-tree order and its second-smallest degree?

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6 Thinking

Proved with GPT-5.6 Thinking and formalized in Lean.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

lean verified statement audited

Lean-checked in the google-deepmind/formal-conjectures repository; maintainer review completed.

Correctness: supported · statement fidelity: audited · peer review: none

Timeline

1. 2026-07-21

   google-deepmind/formal-conjectures (WrittenOnTheWallII)

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

Known method families

argument (source-reported)

Source-reported tools: argument.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.