Show HN: How to Get a Fable CoT for the Jacobian Conjecture Refutation

Since the Jacobian Conjecture refutation was published, readers asked for a published Chain of Thought that would show the mathematical intuition behind the counterexample. No such CoT was released. In a Show HN post titled "How to Get a Fable CoT for the Jacobian Conjecture Refutation," the author described a clean-room reverse-engineering approach built around Claude Fable models, with the surrounding HN discussion also referencing Claude, Codex, and Fable as the tooling stack.

The method is a two-agent loop rather than a single explanation dump. One Claude Fable is given the known result and asked to produce a writeup that leads toward the counterexample without spoilers. A second Fable is then asked to follow that writeup only. If the second model reaches the answer too easily, the author removes detail from the writeup; if it cannot follow the path, the writeup is adjusted in the other direction. Difficulty is tuned until the intermediate document is informative enough to guide reasoning without simply handing over the solution.

For engineers and builders, the interesting part is the evaluation pattern: treat one model as author and another as blind solver, then use success or failure as a signal about how much structure the intermediate document actually contains. That is closer to red-team style validation of an explanation than to ordinary summarization. It also gives a practical way to recover process when only a final result is public and the original reasoning trace is missing.

In competitive context, this sits at the intersection of formal math communication and agent workflows. Labs and tooling ecosystems around Claude, Codex, and Fable already emphasize multi-step reasoning and tool use; this post applies those capabilities to a specific failure mode of scientific publishing—result without process. It is not a claim about which model is strongest on algebra; it is a recipe for reconstructing a usable reasoning path when the original CoT is withheld.

The practical takeaway is narrow and testable. If you need a CoT-like artifact for a hard result that only published the answer, try author/solver clean-room pairs with difficulty tuning instead of asking one model to invent a plausible story after the fact. Watch whether the second agent can reach the counterexample from the writeup alone, and treat that pass/fail as the quality bar for the reconstructed intuition rather than fluency of the prose.