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

A Hacker News user posted a method to generate a Chain of Thought for the Jacobian Conjecture refutation using two Claude Fable instances, one to create a writeup and another to follow it, with the goal of providing mathematical intuition for the counterexample. The approach involves looking in C^3 for a 3:1 cover and using a composition of two functions with Jacobian determinants x and c/x, avoiding Bass–Connell–Wright or Drużkowski normal forms.

Since the publication of the Jacobian Conjecture refutation, many people have asked for a Chain of Thought to be published so they can better understand the mathematical intuition that leads to the counterexample. Since none was published, I tried to "clean room reverse engineer" it: give one Claude Fable the result and ask it to generate a writeup of how to arrive at it without any spoilers, then ask a second Fable to follow the write up, if it's too easy remove details, if it's too hard add hints. I could have simplified further, I stopped because it's time to sleep, and I'm sharing because it gave me some intuition for what's going on. This is what a successful run looks like sadly Anthropic hide Chains of Thought : https://claude.ai/share/80526d56-1c23-407d-8f5c-59a704221454 https://claude.ai/share/80526d56-1c23-407d-8f5c-59a704221454 Intuition This is my understanding of the interesting ideas probably too summarized for Fable to consistently get it without a good harness; take with a grain of salt, I'm not a mathematician; later there is a full prompt that was tested and contains everything needed : No Bass–Connell–Wright or Drużkowski normal forms those are reparametrizations that feel natural in this search but they turn low-complexity examples into high-complexity by trading off degree vs dimension, and the counterexample is low complexity Look in C^3, not C^2, C^2 is probably not interesting enough Look for a 3:1 cover, not 2:1, there's some result due to Euler as always that shows 2:1 will not work Look for a composition of two functions a ratio of polynomials and a shear that have Jacobian determinants x and c/x everywhere, except at x=0 do the standard trick for not defining at a hole and shoving all the problems into that one hole, that's where the 1 + xy comes from Prompt for reproducing CoT Here: https://gist.github.com/SonOfLilit/8882a145048ba260b160568ba... https://gist.github.com/SonOfLilit/8882a145048ba260b160568ba6f48093 prompt-for-reproducing-cot Comments URL: https://news.ycombinator.com/item?id=48986943 https://news.ycombinator.com/item?id=48986943 Points: 1 Comments: 0