Effective Dimensionality from Fisher Information Rank: Operational Validation on Tori, Fractals, Random Graphs, and Coarse-Grained Lattices

We validate Fisher Information Matrix rank as an exact, parameter-free measure of effective spatial dimension. Key results: exact integer dimension on flat tori through d=4, Hausdorff dimension on fractals, a novel disorder direction on random geometric graphs. Code available at github.com/IanD25/D_eff-Test-1.0. Preprint pending arXiv endorsement