Arborescent Eternalism (AE): The Variational and Geometric Foundations of a Fibered Modal Ontology of Spacetime

The block universe interpretation of general relativity treats spacetime as a completed four-dimensional manifold in which all events coexist. This paper identifies a structural lacuna in classical eternalism: while physical laws — particularly in their variational formulations — are defined on spaces of admissible trajectories, the standard block universe suppresses this modal structure, treating the realized history as if it were the only object the laws act upon. The distinction matters. In variational physics, the realized evolution is the stationary solution of a functional defined over an entire space of admissible alternatives. That space is not a computational artifact: it is the domain on which the dynamical principle is formulated. Suppressing it ontologically is not a consequence of the laws — it is an interpretative addition.