Kosniowski's conjecture on fixed points of unitary circle manifolds

Let $M^{2n}$ be a unitary $S^1$-manifold with isolated fixed points, and let $f(n)$ be a positive linear function of $n$. The manifold $M^{2n}$ is a boundary if it represents zero in unitary equivariant bordism.

Kosniowski's conjecture. If $M^{2n}$ is not a boundary, then the number of fixed points is greater than $f(n)$. Kosniowski conjectured that the candidate function is

$$f(n)=\tfrac{n}{2}.$$

This conjecture seeks a linear lower bound on the number of fixed points of a nonbounding unitary circle manifold. The supplied text gives no evidence resolving it.