Infinite-prime independence conjecture for the Weyl-to-Poisson homomorphism

Let $\Phi$ be the homomorphism from automorphisms of the Weyl algebra to polynomial symplectomorphisms constructed by reduction modulo an infinite prime, restriction to centers, inverse Frobenius twisting, and reassembly. Infinite-prime independence conjecture. The homomorphism $\Phi$ is independent of the choice of infinite prime $[p]$.

The conjecture asks whether the reduction-and-Frobenius construction gives an intrinsic homomorphism rather than one depending on the chosen ultraproduct prime. The supplied text presents this as an additional conjecture and gives no evidence of a resolution.