Cosmological Continuity Presentism (CCP): A Generative Spacetime Ontology Compatible with General Relativity

This work develops Cosmological Continuity Presentism (CCP) as a generative ontology of relativistic spacetime that preserves the established local dynamics of General Relativity while advancing a distinct account of temporal structure, causal becoming, and ontological succession. CCP is fundamentally a continuous framework whose core claim is not that relativity is false, but that the ontology of a static block universe is not forced by relativistic formalism. Instead, CCP interprets relativistic spacetime as the emergent representation of an ongoing process of lawful generation in which reality continuously becomes what it next is through uninterrupted causal-temporal evolution. At the deepest ontological level, CCP posits a primitive pre-geometric generative ordering parameter, σ, which labels lawful stages in the production of reality. σ is not fundamentally a scalar field defined on a pre-existing spacetime manifold. Rather, the familiar σ-field description applies only within the emergent geometric regime, where spacetime admits a smooth Lorentzian description and σ can be represented as a constrained scalar field whose level sets define admissible present hypersurfaces. CCP preserves the Einstein field equations, Lorentz invariance, diffeomorphism invariance, and the standard ADM initial-value structure of General Relativity. The existence of admissible temporal orderings follows from the causal structure of globally hyperbolic spacetimes through results due to Hawking–King–McCarthy, Malament, Geroch, and Bernal–Sánchez. CCP interprets σ as a physically calibrated member of the class of smooth Cauchy temporal functions guaranteed by these results, with calibration supplied by the cosmological matter congruence and by a variational constraint derived from the Einstein–matter system. Within the emergent geometric regime, the effective σ field introduces no new propagating gravitational degrees of freedom and does not modify the Einstein equations. Its gradient structure is constrained through the Euler–Lagrange condition ∇μσ ∇μσ = −f(Tμν), where the norm of the gradient is determined by local matter-energy content. Accordingly, σ functions as a constrained scalar whose physical significance derives from the existing Einstein–matter structure rather than from an independent dynamical sector. At any stage of cosmic evolution, CCP assigns ontological existence only to the present physical state represented by the advancing present boundary Σσ. Future states remain ungenerated. Earlier states do not persist as independently existing regions of spacetime; however, this non-persistence concerns the earlier state's specific organization rather than the disappearance of physical continuity itself. Matter, energy, fields, causal influences, and physical consequences continue through lawful transformation, while some consequences remain organized as records accessible within later states. CCP therefore distinguishes between (i) ontological persistence, which is limited to present physical structures and their encoded causal records, and (ii) determinate truth about past events, which may extend beyond what remains physically encoded or recoverable. Present records function as evidential traces and partial physical persistence rather than as the total grounding of all truths about the past. The generated domain M(σ) is a formal representation of generated history and causal ancestry rather than an ontological accumulation of simultaneously existing spacetime regions. Reality itself is understood as a continuously evolving causal-temporal process whose mathematical representation employs foliations and generated domains without implying the co-existence of past, present, and future. CCP treats causal ordering as a structural feature of the generate