We ask how Lorentzian causal structure can emerge from a pregeometric substrate. For arigorously defined class of finite—range, ferromagnetically coupled "chronon" models with quartic norm pinning, we prove the existence, with strictly positive Gibbs probability, of a macroscopic percolating domain D ⊂ M on which the coarse—grained field Φµ is smooth, future—directed,unit—norm timelike (ΦµΦµ = −1, Φ0 > 0) and twist—free. We work on a smooth differentiablemanifold but do not assume Lorentzian signature or a global time field a priori; these arise onD from the dynamics. Under four operational axioms—well-posed local dynamics, finite-speed signalling, acyclic causal order, and stable memory/records—we further prove that no alternative (Euclidean orultrahyperbolic) signature, nor a Lorentzian background lacking a globally unit—norm time field,can sustain such behavior; the Lorentzian, unit—norm phase is therefore exclusive. Finally, we show that "measurement" acts as a boundary-induced selector of this phase: an interface coupling to an aligned apparatus field ΦA admits a unique minimizer, pins the norm and alignment, suppresses twist, and drives any initial state to the aligned phase with exponential convergence; large-deviation bounds quantify high-fidelity selection.Our theorems hold for general (1, d) signatures with d ≥ 1. While the proofs are dimensionagnostic, heuristic coarse-graining and stability considerations suggest d = 3 as the most probable large-scale outcome. Together, these results provide a mathematically controlled foundationfor the emergence and exclusivity of Lorentzian causal structure and for boundary-driven selection (measurement) in pregeometric ensembles.