An Explicit Counterexample to the Rank-Two Poisson Conjecture

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An Explicit Counterexample to the Rank-Two Poisson Conjecture evidence for this event

VibeMathed record: An Explicit Counterexample to the Rank-Two Poisson Conjecture evidence for this event

The paper constructs explicit $R,T,D,S\in\mathbb Q[x,q,p,z]$ defining a Poisson endomorphism of the canonical rank-two Poisson algebra $\mathcal P_2$ that is not an automorphism. Its associated polynomial map preserves the canonical symplectic form, has Jacobian determinant $1$, and has an explicit fiber of exactly three points. Thus $\mathrm{PC}(2)$ is false, and stabilization gives failure of $\mathrm{PC}(n)$ for every $n\ge2$. An appendix further constructs an explicit nonautomorphic endomorphism of the fourth Weyl algebra, proving $\mathrm{DC}(4)$ false. parent of this event

This event attributed to Christopher D. Long

This event attributed to ChatGPT 5.6 Sol

Dixmier conjecture evidence for this event

An Explicit Counterexample to the Rank-Two Poisson Conjecture parent of this event

This event attributed to Claude Fable 5