Entanglement entropy of causal set de Sitter horizons

de Sitter cosmological horizons are known to exhibit thermodynamic properties similar black hole horizons. In this work we study causal set horizons, using Sorkin's spacetime entanglement entropy (SSEE) formula, for a conformally coupled quantum scalar field. We calculate the SSEE Rindler-like wedge of symmetric slab in $d=2,4$ dimensions Sorkin-Johnston vacuum state. find that obeys an area law when spectrum Pauli-Jordan operator is appropriately truncated both as well its restriction wedge. Without truncation, satisfies volume law. This agreement with Sorkin and Yazdi's calculations nested diamonds $\mathbb{M}^2$, where they showed obtained only after truncating spectrum. explore different truncation schemes criterion so