formerly and briefly styled “the Fong Conjecture” — a misattribution, corrected: Danielle Fong never stated it; the statement was machine-proposed. Epitaph in the dustbin.
status: refuted · posed 2026-07-20 ≈11:00 · refuted 2026-07-20 ≈14:00
Refuted by an explicit degree-4 map (“F₄”) from Alexis Gallagher's weighted-lift construction (jacobianfun.org), which produces a counterexample for every generic fiber degree n ≥ 3 — an atlas of 98 of them, degrees 3 through 100, is published there. We transcribed F₄ and verified it on this site's own tools: det JF₄ ≡ 1 exactly; generic fiber degree 4; four distinct preimages over a rational point. The conjecture named its own attack surface (“a quartic fold”) when posed; the attack landed the same afternoon. This page promised to record the result either way. Here it is.
theorem (same day)
Upper half (every n ≥ 3 occurs): Gallagher's weighted-lift family — a one-variable seed p with p(0)=0, p(1)=−c, ∫₀¹p = 0 yields fiber degree deg p + 1. Lower half (n = 2 never occurs): a two-sheeted cover carries a mirror symmetry; symmetric covers are Galois; Galois + constant Jacobian forces an automorphism (Campbell 1973) — recorded on this project hours before the refutation arrived. The conjecture was wrong; the question was right; the two halves of the answer came from different people working the same 24 hours. That is the system functioning.
Ledger and machine verification: jacobianconjectures.com (check C9 = F₄) · constitution: fablehaven.cc — corrections are recorded, never erased.