AI-assisted Jacobian counterexample in dimension three
The Ulam writeup reports a polynomial map C³→C³ with constant nonzero Jacobian determinant −2 and three distinct points sharing one image.
Original report: 2026-07-20The Jacobian conjecture
Does a polynomial self-map with constant nonzero Jacobian necessarily have a polynomial inverse?
Progress records 1
Understand the problem ↓1 record · How we rate progress
Understanding the problem
Read the background
Does a polynomial self-map with constant nonzero Jacobian necessarily have a polynomial inverse? Dimension must be specified.
Why it matters
A precise target for comparing mathematical claims, their baselines, and the documented contribution of AI.
What counts as progress
A sourced theorem, construction, algorithm, bound, or substantive formalization with its assumptions and AI role stated.
What to watch for
- Check the exact hypotheses and compare with the stated prior baseline.
- Distinguish a source claim, an available proof, and a reproduced verification.
- Retain human contributions, competing work, corrections, and withdrawals.
Background review: 2026-10-11. Selected sources:
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Publication dates and editorial changes.