Relative Duality Data under Hierarchical Coarse-Graining: An Exact Finite Cellular Laboratory

This work develops an exact finite cellular laboratory over (\mathbb{F}_2) to investigate relative homology and duality data under hierarchical coarse-graining. It constructs a parameterized family of cellular chain maps, analyzes relative degree and the preservation of the relative fundamental class, studies the action of (D_4) symmetry, and verifies a three-scale composition law within an explicitly defined finite hierarchy. The results establish finite algebraic statements within the specified model and are not presented as a universal classification of physical systems. A computational audit script and its output are included to support reproducibility. This work continues the research program initiated in Work I: https://doi.org/10.5281/zenodo.22557436.