Energy as Structural Reconfiguration in a Continuity-Deficit Ontology: An Action-Based Extension of the Anti-Shape Field Framework

This preprint extends the continuity-first ontological framework in which matter is interpreted as the observable projection of structural continuity deficit (Anti-Shape). The present work reinterprets energy not as an independent substance but as the measurable structural intensity of configuration within the Anti-Shape scalar field.A covariant scalar-field action is introduced, and the associated stress–energy tensor is derived. Energy density emerges from spatial gradients, indexed reconfiguration rates, and structural potential contributions of the Anti-Shape field. Conservation laws are shown to arise from diffeomorphism invariance rather than being assumed independently.Mass–energy equivalence is reinterpreted as the relation between static deficit localization and dynamic field excitation. The framework preserves compatibility with Einstein field equations while maintaining continuity primacy at the ontological level.This article represents Article 3 in the Continuity–Anti-Shape research program.