The Fractal Ontology: Black Hole Interiors as Physical S2, Nested Singularities as Recursive S1 Events, and the Scale-Invariant Architecture of Reality _The Third Paper in the Tripartite Transitional Ontology Series_

This paper extends the Tripartite Transitional Ontology framework (Beyond Being and Non-Being: A Three-State Model of Ontological Transition - Beard, 2026a) to propose a scale-invariant, recursive ontological architecture in which the three-state structure of S1 (the Plenum), S2 (the Absolute Void), and S3 (the Existential Event Horizon) repeats at every physical scale, nested within itself indefinitely. We propose that the interior of a black hole constitutes a physically realized local S2, a region of causal inaccessibility whose structural properties mirror the formal properties of the Absolute Void established in Paper 1. The black hole's event horizon serves as a local S3 boundary, and the singularity at the black hole's interior constitutes a nested S1 event, a new region of structured existence arising within the local void. We further propose that our observable universe is itself a nested S1 event within a larger S2 framework, bounded by a cosmological S3 horizon, making our Big Bang structurally equivalent to a singularity formation event viewed from within. This recursive fractal architecture resolves the regress problem of Paper 1 (how S2 can be both logically necessary and physically real) by providing a physically observable instantiation of S2 at every scale. The framework is shown to be consistent with the Holographic Principle, Ptolemy's Theorem as a geometric proof of concept for S3's lawgiving function, black hole thermodynamics, and the cyclic cosmological model of Paper 2 (Compression, Expansion, and the Cyclic Universe - Beard, 2026b).