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

The Jacobian Conjecture refutation left a gap many readers felt immediately: people asked for a published **Chain of Thought** that would show the mathematical intuition behind the counterexample, and none appeared. The Show HN post responds to that demand with a practical method rather than a finished proof narrative. Its title is direct—**How to Get a Fable CoT for the Jacobian Conjecture Refutation**—and the work sits at the intersection of formal math, public proof culture, and tool-assisted reasoning on HN.

Technically, the approach is a **clean room reverse engineer** of the missing CoT. One **Claude Fable** is given the result and asked to produce a writeup that explains how to arrive at it without spoilers. A second Fable is then asked to follow that writeup alone. Difficulty is tuned by editing the writeup: if the second model solves it too easily, details are stripped; if it fails, the guide is enriched until the path is hard but recoverable. The product mechanic is not “generate an explanation once,” but an iterative teacher–student loop between two isolated Fables that pressure-tests whether the written intuition is sufficient.

For engineers and builders, the interesting part is the evaluation design. You get a reusable pattern for recovering **missing intermediate reasoning** when only the final claim is public: separate the model that knows the answer from the model that must rediscover it, and use success or failure of the second as a signal about how much structure the writeup still leaks. That is closer to red-team prompt design and curriculum construction than to ordinary summarization.

In competitive and market context, this lands in the same lane as other Claude, Codex, and Fable experiments people already share on HN: tooling that turns opaque model outputs into inspectable procedures. The Jacobian Conjecture case is a high-stakes stress test because the target is genuine mathematical intuition, not a coding puzzle with a known test suite. Whoever can reliably extract and grade such CoTs gains an edge in education, auditability, and research tooling around hard proofs.

The practical takeaway is to treat the dual-Fable loop as a template: result-holder Fable writes a spoiler-free path; solver Fable tries it; adjust detail until the path is neither trivial nor impossible. What to watch next is whether this method generalizes beyond this counterexample—whether other unpublished CoTs for major results can be reconstructed the same way, and how stable the difficulty edits remain when a third independent model or a human follows the same writeup.