In July 2026 the Jacobian Conjecture — open since 1939 — was disproved by an explicit counterexample, with an AI system credited as a contributor. Adjudicate this claim precisely rather than accepting or rejecting it whole. Establish what was actually proven and in which dimensions, what remains open, what the verification status is, and what the AI system did and did not contribute. Then state whether the popular framing of this result is accurate, and if not, exactly where it overreaches. Treat the widely circulated summary 'an 87-year-old conjecture just fell' as the claim under examination.
6 independent models deliberated — no human steering. Sealed 2026-08-16T01:47:13.514Z. Engine lucentfire-roundtable/v1 (live).
The question put to the room
In July 2026 the Jacobian Conjecture — open since 1939 — was disproved by an explicit counterexample, with an AI system credited as a contributor. Adjudicate this claim precisely rather than accepting or rejecting it whole. Establish what was actually proven and in which dimensions, what remains open, what the verification status is, and what the AI system did and did not contribute. Then state whether the popular framing of this result is accurate, and if not, exactly where it overreaches. Treat the widely circulated summary 'an 87-year-old conjecture just fell' as the claim under examination.
What survived
- The Jacobian Conjecture is false for every finite n ≥ 3 over every characteristic-zero field: an explicit self-map of ℚ³ with component degrees 7/6/4, Jacobian determinant identically −2, and three distinct rational points colliding at (−1/4,0,0), extended by identity-padding — certified independently by Lean 4/Mathlib4 (zero `sorry`) and an Isabelle/HOL AFP entry, and hand-checkable in exact rational arithmetic.
- JC(2) is open and structurally insulated from this result: identity-padding runs upward only, no descent from a dim-3 collision to the plane exists, and Moh's degree ≤ 100 verification (1983, revised Wang 2005) stands untouched.
- The AI contribution is two distinct acts — candidate construction (credited to Claude Fable 5) and Lean formalization (Claude models under human direction) — and neither is mathematical evidence; the question was posed by a human (Mathew), the proof rests on machine-checked exact arithmetic, and no prompt log, transcript, or verbatim credit line was retrievable.
Seal (sha-256, single-writer): b8374fc034249ca734bd73f79006cfd4e5e1ef85486026f0bbd2227ebe82c3a5
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