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Open-problem programVerified

2026 Jacobian counterexample reproduction

Reproduce the announced polynomial map in three variables, verify that its Jacobian determinant is the nonzero constant -2, and verify that three distinct rational points have the same image.

Why this problem

A small, decisive, independently reproducible calibration of the entire evidence pipeline. This is prior work, not a Proof Factory discovery.

Verification contract

Exact symbolic identity and three rational witness evaluations

Tracking
Difficulty
3/10
Attempts
1
Last attempt
2026-07-20 15:20 UTC
Source status
disproved
External validation
none
Techniques and harnesses
symbolic differentiationexact rational arithmeticcollision witness
Resumable campaign memory

Research map

1 epochs · 0 promising · 1 blocked · 0 ruled out
Next session checkpoint

Package the script and dependency lock as the calibration certificate.

First action: Package the script and dependency lock as the calibration certificate.

Stop or redirect when: The planned discriminator resolves the route.

Open leads
  • No open lead is checkpointed.
Strategy registry
  • unspecified
    Differentiate the three displayed coordinate polynomials symbolically, factor the determinant, then evaluate the map at the three announced rational points using exact arithmetic.
Ruled out, with scope
  • Nothing has been rigorously ruled out yet.
Complete history

Attempts on this problem

2026-07-20 15:20 UTCOpen-problem program · Duration unavailable

2026 Jacobian counterexample reproduction

Differentiate the three displayed coordinate polynomials symbolically, factor the determinant, then evaluate the map at the three announced rational points using exact arithmetic.

What this run accomplished

Independent reproduction returned determinant -2 and the same image (-1/4, 0, 0) for all three distinct inputs.

Next: Package the script and dependency lock as the calibration certificate.