Equivariant factorization-homology realization of the twisted Dennis trace

Let $R$ be a $C_n$-ring spectrum. The twisted Dennis trace is a map

$$\textnormal{K}_{C_n}(R)^{C_n} \to \operatorname{THH}_{C_n}(R).$$

Horev's identification gives

$$\operatorname{THH}_{C_n}(R) \simeq \Phi^{C_n} \int_{S^1_{\mathrm{rot}}} R,$$

where $\int_{S^1_{\mathrm{rot}}} R$ is the $C_n$-equivariant factorization homology of the circle with rotation action and coefficients in $R$. Equivariant factorization-homology realization conjecture. The twisted Dennis trace of Corollary arises from a $C_n$-equivariant map

$$\textnormal{K}_{C_n}(R) \to \int_{S^1_{\mathrm{rot}}} R.$$

Such a map would refine the twisted Dennis trace before taking $C_n$-geometric fixed points. The conjecture is motivated by the equivariant factorization-homology description of twisted topological Hochschild homology; no resolution is given here.