The dense basic-set existence conjecture for quantization

Let $M$ be a symplectic manifold and ${\cal B}$ a basic set such that $\wp({\cal B})$ is dense in $C^{\infty}(M)$.

Dense basic-set existence conjecture. There exists a nontrivial quantization of

$$\big({\cal P}(M),{\cal B}\big).$$

This conjecture is motivated by the torus example and is intended as a complementary possibility to the finite-dimensional obstruction conjecture. The paper offers it as a speculative proposal; its general validity remains open.