Written on the Wall II, Graph Conjecture 109

Precise statement

Must every connected graph satisfy the proposed upper bound on its independence number in terms of residue and largest induced-bipartite-subgraph order? The family $\overline{K}_{2r+1} \vee (K_r \sqcup K_r)$ violates it for every $r \ge 3$.

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 Sol Max (Codex)

The infinite counterexample family was found with GPT-5.6 Sol Max running in Codex; verified in Lean plus independent Python and C++ enumeration.

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

Verification boundary

lean verified statement audited

Lean-checked disproof in the google-deepmind/formal-conjectures repository, with independent computational enumeration.

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

Timeline

1. 2026-07-28

   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

construction (source-reported)

Source-reported tools: construction.

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.