Light cones from causal links: an area law, its logarithmic correction, and null convergence in causal set theory

This paper shows how a light cone can emerge from a Lorentz-invariant causal set even though no two sprinkled elements are exactly null related. By studying the links of a single element, it derives an area law, identifies curvature through nonlocal null-weighted observables, and shows that Ricci focusing appears at first order while Weyl tidal structure emerges only at second order. The result offers a concrete picture of continuum geometry as a relational structure reconstructed from causal order rather than assumed at the microscopic level.