Resolves as YES if there is strong evidence that OpenAI discovered the first valid proof of the Collatz Conjecture before January 1st 2026. Only proofs made public before 2026 are considered, and the public release date determines which proof is deemed the “first.” If at least one candidate proof from OpenAI is made public before the end date but its validity remains uncertain, the end date can be extended until the proof’s validity is resolved. Both proofs that demonstrate the conjecture or demonstrate that it's undecidable are acceptable in the context of this question.

If another entity makes a proof public first and that proof is considered valid, this question automatically resolves as NO. Similarly, if no publicly known OpenAI proof emerges before January 1st 2026, the question resolves as NO.

Examples of what qualifies as a "proof from OpenAI” include, but are not limited to:

• Papers published to arXiv (or other preprint servers) with OpenAI researchers listed as authors.
  
  

• Peer-reviewed journal or conference publications with (strongly) OpenAI-affiliated authors.
  
  

• White papers or technical reports released on official OpenAI channels (e.g., blogs, GitHub, or websites).
  
  

• Work using proprietary OpenAI models (not publicly available), where the researchers have privileged access and rely on OpenAI’s own compute resources or those provided through partnerships (e.g., Microsoft). Proofs run on third-party servers outside such partnerships (e.g., a university cluster) do not qualify under this condition.
  
  

A public release of any document or presentation that claims to prove the Collatz Conjecture—produced (or co-produced) by OpenAI researchers and using OpenAI resources—will be sufficient to trigger a YES resolution if no other valid proof has been released prior to it. If the validity of an OpenAI proof remains uncertain by January 1st 2026, the resolution date may be postponed until its validity is established.