The Dark Universe in Finite-Resolution Physics

This work develops a carrier-dependent extension of Finite-Resolution Physics and applies it to the dark universe. The central proposal is that the familiar matter-like and vacuum-like dark components need not be introduced as two independent fundamental additions to Einsteinian gravity. Instead, they can arise as different metric representations of a single hierarchical continuation sector that is jointly stabilized with the real carrier supporting the ordinary gravitational branch.

The paper first develops the native dynamics of a hierarchical continuation carrier in terms of refinement, descent, branching, and multilevel coherence. It then constructs a mixed real-hierarchical regime and distinguishes structural interlocking from a phenomenological interaction inserted directly into field equations. In this setting, the ordinary metric description can remain valid while failing to exhaust the full continuation structure. A source-form metric representation of the hierarchical sector produces two important classes of observable shadow: a collisionless kinetic component with dark-matter-like behaviour and a scalar component with vacuum-like behaviour. These can remain dynamically interlocked even when their metric contributions are additive.

For the minimal interlocked branch, total conservation restricts the exchange between the two metric shadows rather than allowing an arbitrary interaction current. In homogeneous cosmology, the kinetic density, scalar density, and exchange rate can be reconstructed from the residual expansion history. The framework also yields a specifically hierarchical observational requirement: dark-sector reconstructions obtained at different admissible resolutions should not vary independently, but should satisfy one coherent descent relation across resolution. This provides a way to distinguish a genuinely hierarchical origin from a merely flexible effective-source fit.

The manuscript therefore offers a structural explanation, within Finite-Resolution Physics, of how Einsteinian gravity can coexist with a dark sector exhibiting both matter-like and vacuum-like effects without requiring the Einstein operator itself to be modified. It also separates results that follow from the carrier structure from those that depend on particular metric, kinetic, scalar, cosmological, or self-similar realizations. The work does not yet fix absolute dark-sector abundances, halo profiles, production laws, or universal refinement exponents; these are left to more specific realizations and empirical tests.

This is an extended archival manuscript containing the full derivational development and the assumptions, limitations, and observational consequences of the real-hierarchical construction.