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) supplies precisely these two pieces — becoming is actualization, real and objective; the basis is einselected by the causal past of each event — without refounding the programme: TA inherits its machinery and adjoins to it an ontological referent and a basis selector. We present this interface as a consistency bridge, not a derivation: TA derives neither the emergent geometry (the Hauptvermutung — the conjecture that order and number fix a unique continuum limit — partially resolved, remains inherited) nor the complete quantum dynamics (the rate law of actualization remains open). The contribution is ontological and unifying — it identifies in one single process the objective-collapse "flash", the grown element of the causal set, and actualization.