Zyskind's factory

Posted on 20 July 2026 at 22:40 UTC under the line “the jacobian conjecture is not merely false, it is factory false”. It lists 16 maps said to be exactly checked: the seed (Alpöge's map), nine base maps from three branches, three compositions in ℂ³ and three products into ℂ⁶ and ℂ⁹. Some have coefficients in a number field. The example N2 has $(m,r,C)=(2,1,12)$ and $h=u+u^2A$ with $u^2-4u+6=0$, so $u\in\mathbb Q(\sqrt{-2})$, and fiber degree 4.^[1]

If the claim holds, every factory output is a Keller map of ℂ³ with at least three preimages over a general point, and so refutes JC₃. The general claim has no written proof. The Fong–Fable ledger reports re-verifying branch N2 (its denominators cancel modulo $u^2-4u+6$, and $\det=-12=-C$) and leaves the other 15 maps unverified.^[2] The research for this page checked the seed by hand. At $(m,r)=(1,1)$, $h(A)=3+9A$, the factory map is Alpöge's after $z\mapsto3z$ and rescaling outputs, so the factory's first member is Alpöge's map.

From the formulas, every base map is $\mathbb G_m$-equivariant with source weights $(m,-1,-(m+1))$. That includes the number-field members, so none of them is a counterexample without torus symmetry.

1. ↑ G. Zyskind, X post of 20 July 2026 (read through the fxtwitter mirror).
2. ↑ D. Fong and Claude Fable 5, claims ledger.