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The conjecture (Belov-Kanel–Kontsevich) that every automorphism of the n-dimensional polynomial Poisson algebra is a Poisson polynomial automorphism, i.e. the classical limit of the Dixmier conjecture. Claims about its truth, reformulations, or its stable equivalence to the Dixmier and Jacobian conjectures belong here.

Stable equivalence does not directly transfer a dimension-3 Jacobian counterexample to any Dixmier rank.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Jacobian conjecture Dixmier conjectureimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

The Jacobian, Dixmier, and Poisson conjectures are stably equivalent.

UnassessedNo current assessment. Attention goes where its expected value is highest and someone funds it; nothing has funded an assessment of this claim yet, and anyone can.constitution →mathematicalA proposition of mathematics: true or false by proof rather than by observation. Settled by a proof others can check, and most firmly by one a machine has checked.constitution →Dixmier conjecture Jacobian conjecture Algebraic geometryimportance · minorImportance 0.40, from 0 to 1 · minor: narrow or largely settled, cheap to get right. Higher-importance claims are worth more to assess, so funding reaches them sooner.constitution →

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