A Lorentz-Invariant Phase Anchor and a Dirac-Compatible Spinorial Lifting Scaffold

This work develops a minimal relativistic phase framework that connects internal periodicity, de Broglie modulation, and a Dirac-compatible branch structure within a single kinematic construction.

Starting from a Lorentz-invariant internal phase anchor, the analysis shows that the de Broglie wave can be interpreted as the observer-frame modulation of an underlying proper-time periodicity, rather than as an independent ontological wave imposed from outside. This yields a compact geometric picture in which matter-wave phase arises from relativistic unfolding of an intrinsic internal clock.

To extend this structure beyond the scalar phase level, a minimal half-angle lifting is introduced through a phase variable ΘΘ, defined only at the level required to construct the branch scaffold. No strong physical interpretation of ΘΘ is imposed in this paper. Within this restricted setting, the lifted phase naturally generates a four-branch organization that is compatible with the formal sign structure of the Dirac plane-wave sectors. The purpose of this construction is not to claim a full derivation of the Dirac equation, nor a strict one-to-one identification of all branches, but to establish a compact relativistic phase scaffold that is structurally consistent with Dirac-type splitting.

The main contribution of this paper is therefore a kinematic bridge: from Lorentz-unfolded internal periodicity, to de Broglie phase modulation, to a minimal Dirac-compatible branch architecture. This provides a controlled intermediate layer between scalar relativistic phase and spinorial structure, while leaving detailed physical interpretation, strict branch mapping, and full dynamical completion to subsequent work.

This paper is intended as a structural foundation for later developments in the Vacuum Fluid Theory (VFT) program, especially those concerning the emergence of spinorial sectors, relativistic morphology, and the relation between internal phase organization and observable quantum branches.