Claude Fable 5 Produced a Hand-Checkable Counterexample to the 1939 Jacobian Conjecture

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Anthropic mathematician Levent Alpöge posted on July 19 that he and collaborator Matthew, working with Claude Fable 5, found a concrete degree-7 counterexample in three variables to the Jacobian Conjecture, open since 1939: F(x,y,z) = ((1+xy)^3 z + y^2(1+xy)(4+3xy), y + 3x(1+xy)^2 z + 3xy^2(4+3xy), 2x - 3x^2 y - x^3 z), with det(J_F) = -2 yet three distinct points mapping to the same image. Mathematicians had estimated any counterexample would need degree ~200. The HN thread hit 538 points and 334 comments in 11 hours, with the central dispute being how much of the search was model-generated versus human-directed.