Fu's power series conjecture for invariant valuations on complex space forms

Let $b\mathbb{CP}^n_\lambdad$ be the complex space form of constant holomorphic curvature $4\lambda$, with invariant valuation algebra $\mathcal{V}(\mathbb{CP}^n_\lambda)^{G_\lambda}$. Define Tutte's series by

$$\tau(\lambda):=\sum_{i=1}^\infty \frac{2(4i+1)!}{(i+1)!(3i+2)!}\lambda^i=\lambda+3\lambda^2+13\lambda^3+68\lambda^4+399\lambda^5+\ldots$$

For $k\geq 1$, let $\bar f_k^\lambda(t,s)$ be the degree-$k$ part of the expansion of

$$\log\left(1+t+s+\tau(\lambda)\right),$$

where $t$ has degree $1$, $s$ has degree $2$, and $\lambda$ has degree $-2$. Fu's power series conjecture. The algebra of invariant valuations on $\mathbb{CP}^n_\lambda$ should be isomorphic to

$$\mathbb{R}[[t,s]]/(\bar f_{n+1}^\lambda,\bar f_{n+2}^\lambda).$$

This conjecture proposes a curved analogue of Fu's presentation of the algebra of translation-invariant, unitary-invariant valuations on $\mathbb{C}^n$, with Tutte's series encoding the dependence on the curvature parameter. Its status is not resolved by the supplied source context.