A Minimal Cosmological Benchmark for the Fractal Consistency Law

A Minimal Cosmological Benchmark for the Fractal Consistency Law Background expansion, linear growth, structural dark-sector unification, and a falsifiable geometric-textural benchmark Structural Foundations of the Fractal Consistency Law This paper presents a reordered and corrected cosmological benchmark for the geometric-textural sector of the Fractal Consistency Law (FCL). Rather than adding dark matter and dark energy as independent substances, the benchmark interprets the dark sector as the late-time manifestation of a textured geometric substrate encoded by a macroscopic field D. A covariant effective action is formulated, the textural potential is structurally derived from a coarse-grained restoration cost associated with microscopic spectral imbalance, the background branch is written as a closed dynamical system, and the linear subhorizon sector is described through the coupled effective functions μ(k,z), η(k,z), and Σ(k,z). The resulting observable package is jointly constrained and therefore jointly falsifiable. The present version corrects the internal order of the manuscript, harmonizes notation across all sections, restores clear equation display and numbering, and rewrites the appendices so that they function as well-defined technical closures rather than as informal add-ons.