alt Hacker NewsSome speculation in this Claude chat: https://claude.ai/share/22abed98-d9af-43c5-9881-b19e009a07b0
linked from here: https://x.com/b_shrir/status/2079094004885668003?s=20
Very short version: there’s an existing false counterexample in the literature which holds almost everywhere except at a pole. It looks like Fable used this polynomial as a base & extended it in a way that eliminated the pole whilst preserving the structure.
I'm going to paraphrase what GPT told me: Consider the canonical degree 3 (subvariety of the trivial P1 bundle consisting of zeros) cover of the projectivization of homogenous polynomials of degree 3 in 2 variables (so it's a 3fold cover of P^3). The top space is P1 x P2 and if you take a standard affine open of the base and look at the cover over that restricted to a subset where the zero of the cubic is simple you get the map for some choice of coordinates...
I honestly have no idea if it's correct lol I didn't check it (I should given I actually work in AG) but it doesn't look impossible at first sight