OpenAI says its GPT-5.6 Sol Ultra mode generated a proof for the Cycle Double Cover Conjecture, a long-standing graph-theory problem, in under an hour. The claim is notable, but it remains a claim until mathematicians complete independent peer review of the published proof.
The model launched July 9 as part of the GPT-5.6 family, which includes Sol, Terra, and Luna tiers. According to OpenAI, Sol Ultra is the highest-capability setting: it coordinates multiple agents in parallel for tasks where additional compute and token use are acceptable. OpenAI’s published benchmark table lists Ultra at 91.9% on Terminal-Bench 2.1, an evaluation of complex command-line tasks.
The Cycle Double Cover Conjecture asks whether every bridgeless graph can have its edges covered by cycles so that every edge appears exactly twice. It has resisted a general proof for decades.
OpenAI has made the prompt and resulting proof available for scrutiny, according to reports from Crypto Briefing and other outlets. That is the appropriate next step, not a victory lap: a model-generated proof can look complete while hiding an invalid assumption, an omitted edge case, or a definition mismatch. Until graph theorists verify the argument, the correct description is that GPT-5.6 Sol Ultra produced a purported proof.
That distinction also applies to claims connecting the model to a specific numbered Erdős problem. Crypto Briefing reported that no independently confirmed evidence presently links Sol Ultra to a verified solution of Erdős problem #793.
OpenAI says GPT-5.6 Sol, Terra, and Luna are also available through its API. Sol costs $5 per million input tokens and $30 per million output tokens; Terra is priced at $2.50/$15, and Luna at $1/$6. Ultra is a capability setting rather than a separately priced API model, and its parallel-agent approach can raise total token consumption substantially.
A Solana meme token using the model’s name has also appeared, but Crypto Briefing reported near-zero activity and no OpenAI affiliation. It has no bearing on the model release or Microsoft 365 Copilot deployment.
Admins evaluating GPT-5.6 should treat the math story as unverified research news and assess the Copilot and API changes on normal security, cost, and output-validation grounds.
The model launched July 9 as part of the GPT-5.6 family, which includes Sol, Terra, and Luna tiers. According to OpenAI, Sol Ultra is the highest-capability setting: it coordinates multiple agents in parallel for tasks where additional compute and token use are acceptable. OpenAI’s published benchmark table lists Ultra at 91.9% on Terminal-Bench 2.1, an evaluation of complex command-line tasks.
Proof claim needs outside validation
The Cycle Double Cover Conjecture asks whether every bridgeless graph can have its edges covered by cycles so that every edge appears exactly twice. It has resisted a general proof for decades.OpenAI has made the prompt and resulting proof available for scrutiny, according to reports from Crypto Briefing and other outlets. That is the appropriate next step, not a victory lap: a model-generated proof can look complete while hiding an invalid assumption, an omitted edge case, or a definition mismatch. Until graph theorists verify the argument, the correct description is that GPT-5.6 Sol Ultra produced a purported proof.
That distinction also applies to claims connecting the model to a specific numbered Erdős problem. Crypto Briefing reported that no independently confirmed evidence presently links Sol Ultra to a verified solution of Erdős problem #793.
The Windows and Microsoft angle
For Windows users, the more immediate development is not graph theory. OpenAI says GPT-5.6 is becoming the preferred model in Microsoft 365 Copilot across Word, Excel, PowerPoint, Copilot Chat, and Cowork. Microsoft 365 users should therefore expect the model family to appear in routine drafting, spreadsheet analysis, presentation work, and other Copilot-assisted workflows as rollout proceeds.OpenAI says GPT-5.6 Sol, Terra, and Luna are also available through its API. Sol costs $5 per million input tokens and $30 per million output tokens; Terra is priced at $2.50/$15, and Luna at $1/$6. Ultra is a capability setting rather than a separately priced API model, and its parallel-agent approach can raise total token consumption substantially.
A Solana meme token using the model’s name has also appeared, but Crypto Briefing reported near-zero activity and no OpenAI affiliation. It has no bearing on the model release or Microsoft 365 Copilot deployment.
Admins evaluating GPT-5.6 should treat the math story as unverified research news and assess the Copilot and API changes on normal security, cost, and output-validation grounds.
References
- Primary source: Pluang
Published: 2026-07-13T00:00:00+00:00
OpenAI's GPT-5.6 Sol Ultra solves major math co... | Pluang
OpenAI's latest model, GPT-5.6 Sol Ultra, has quickly solved the longstanding Cycle Double Cover Conjecture in graph theory, completing the proof in under an hour using advanced parallel reasoning. This achievement is significant as the conjecture has puzzled mathematicians for decades, and...pluang.com - Independent coverage: Crypto Briefing
Published: 2026-07-13T22:12:26+00:00
GPT-5.6 Sol Ultra tackles major math problems as opportunistic meme token launches on Solana
OpenAI's GPT-5.6 Sol Ultra solved the Cycle Double Cover Conjecture in under an hour, while a namesake Solana meme token struggles with zero liquidity.cryptobriefing.com - Related coverage: remio.ai
OpenAI Paper Claims GPT-5.6 Sol Ultra Proved the Cycle Double Cover Conjecture
A careful look at OpenAI's claimed proof of the Cycle Double Cover Conjecture, what the paper establishes, and why independent verification matters.
www.remio.ai
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OpenAI's GPT-5.6 Sol Ultra Proves 50-Year-Old Math Conjecture in Under an Hour | KuCoin
OpenAI just did something that makes every “AI will take your job” headline feel quaint. Its newest model, GPT-5.6 Sol Ultra, generated a machine-verified proofwww.kucoin.com - Related coverage: axios.com
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