Spectral union conjecture for monodromy operators of neutral renewal equations

Let $A\colon \mathbb{R} \to \mathbb{R}^{d \times d}$ be a $\tau$-periodic function whose components have bounded variation and are continuous from the right. Let $U$ be the monodromy operator of the neutral renewal equation, interpreted as specified for the case in which $f$ is constant, and let $U_{\mathbb{C}}$ denote its complexification. Spectral union conjecture. The spectrum of $U_{\mathbb{C}}$ is

$$\sigma(U_{\mathbb{C}})=\overline{\bigcup_{t\in\mathbb{R}}\sigma(A(t))}.$$

The numerical experiments suggest that the spectrum of the evolution operator is approximated by the union of the spectra of the coefficient matrices over one period. The conjecture concerns the exact spectral description for periodic, possibly discontinuous coefficient functions, and no resolution is given in the source.