An ontology for causal-set dynamics: Becoming as actualization, the basis as causal past

Abstract

The causal-set programme proposes that spacetime is, at bottom, a discrete poset whose Lorentzian geometry emerges, endowed with a covariant sequential growth dynamics. It leaves open, however, two points that an ontology must settle: the status of the "becoming" of growth (a computational procedure or a real process?), and the basis of its quantum version (quantum sequential growth, QSG, does not specify the basis of the histories). We show that the theory Time–Actualization (TA) proposes an ontological answer: becoming is posited as real actualization, while the basis is selected by the couplings carried by the causal past, where that monitoring supplies a sharp basis. This identifies an environment within the ontology; it does not derive its coupling content or construct the full quantum dynamics. We present the interface as a consistency bridge, not a refoundation. The emergent geometry and its Hauptvermutung remain inherited, and the dynamical law of actualization remains open. The proposed unification concerns a common process reading of flashes, system actualizations and causal-set growth; their different rates still require an explicit interface.