Fable 5 Model Release and Availability: Counterexample Discovery, Autonomous Workflows, and Permanent Availability

Anthropic's Claude Fable 5 model has recently garnered significant attention. Mathematician Levent Alpoge announced on Twitter that Fable 5 found a counterexample to the Jacobian conjecture, which has puzzled mathematicians for 85 years since its proposal in 1939. The counterexample is a polynomial map from C³ to C³ with a constant Jacobian determinant of -2, but maps three distinct points to the same image point, thus disproving the conjecture. The tweet received over 5 million views, and multiple mathematicians have verified the result, though it has not yet undergone formal peer review.

On the application side, Claude Code creator Boris Cherny demonstrated how to build autonomous workflows using Fable 5's /goal and /loop commands. He submits dozens of PRs daily through hundreds of AI agents, where the model writes code and humans handle acceptance. /goal defines the endpoint and iterates automatically, while /loop repeats tasks on a schedule; together they enable long-term autonomous work. The tutorial recommends configuring local context to let the model remember personal preferences and using Fable 5 only for high-value tasks to save costs.

Anthropic announced on July 20 that Fable 5 is permanently available, included in Max and Team Premium subscription plans (with a 50% usage cap), while Pro and Team standard users receive a one-time $100 credit as compensation. Previously, Anthropic planned to discontinue Fable 5, but changed strategy due to OpenAI GPT-5.6 Sol's low-price competition and the release of Moonshot AI's Kimi K3. Kimi K3 is a 2.8 trillion parameter open-source model, ranked first in the frontend code arena, with API prices less than one-third of Fable 5's, posing a challenge to Silicon Valley's high pricing model.