Axiomatic Hierarchy of the VFT Programme: Matter as Field Depletion, the Emergence of Gravitation, and the Propagation Structure of the Cosmological Field Ground

This paper formulates the axiom layer of the Verarmungsfeldtheorie (vft) programme in a form suitable for later mathematical realization. It does not present a completed dynamical theory; it isolates the non-negotiable structural commitments that any admissible realization of the programme must satisfy. The axiom layer does not begin with relational inertia. It begins with matter as eld depletion: material manifestations are stable local state-forms of a universal cosmological eld ground, in which eld-ground energy is bound into the form operationally identied as matter and the corresponding unbound eld balance is lo- cally depleted. Rest mass is read as the locally invariant signature of a stable eld-ground depletion mode. The ve axioms then read in directed order: a universal eld ground (Ax- iom I); matter as eld depletion (Axiom II); gravitation as the emergent eect of depletion gradients (Axiom III); variable inertia, depending on the local eld state (Axiom IV); and depletion-bounded propagation, with the invariant speed cas the limiting propagation speed of massless eld excitations and a Lorentzian inertial growth for massive manifestations as a limiting response of depletion-bound propagation (Axiom V). The relational character of inertia is not an axiom but a consequence: a depletion manifestation cannot possess an in- ertial response independently of the eld state from which it arises. The paper deliberately separates three layersaxiom, realization, and empirical projectionand sets out the rst in detail, preparing the second through a structured matrix of eight realization classes and a system of twelve global consistency gates classied as hard exclusion, strong tension, or implementation burden. Comparisons with historical and technical literature are presented as context, not as sources.