Black Holes as Singular Points of a Fractal Spacetime Manifold

This record contains a complete academic preprint (LaTeX source and compiled PDF) together with a companion theory overview document, presenting a phenomenological mathematical framework in which black holes are interpreted as singular cusp points of a fractal spacetime manifold. Theoretical contributions Spacetime is modeled as a fractal metric-measure space with statistical self-similarity Black hole singularities are reinterpreted as cusp points of vanishing Hölder regularity, rather than breakdowns of geometric structure A renormalization-group (RG) flow for an effective roughness parameter H is introduced, with three fixed points: UV singularity (H = 0), critical crossover (H = Hc), and IR attractor (H = H*) The event horizon is characterized as a crossover (inflection) surface in the roughness profile, compatible with the equivalence principle The Bekenstein–Hawking area law receives a fractal correction governed by the effective Hausdorff dimension of the horizon Three classes of falsifiable observational predictions are proposed: mass distribution scaling, ringdown spectrum corrections, and DFA roughness signatures Archive contents paper/fractalblackₕolesᵥ2. 1. tex — Full LaTeX source of the mathematical preprint paper/fractalblackₕolesᵥ2. 1. pdf — Compiled PDF of the main paper (10 pages) overview/theoryₒverviewᵥ2. 1. pdf — Theory overview in accessible professional language, no formulas (6 pages) CITATION. cff — Machine-readable citation metadata README. txt — Archive description and structure LICENSE. txt — CC BY 4. 0 license Methodological note The manuscript is intentionally code-free and focuses exclusively on mathematical structure and conceptual consistency. It maintains explicit ontological layering: definitions, postulates, lemmas, theorems, hypotheses, and remarks are clearly separated throughout. The work is offered as a phenomenological scaffold for independent academic audit and critique — no claim of a complete quantum-gravity theory is made. MSC 2020: 83C57, 28A80, 83C75, 81T17