The Topographical Subset Ontology: A Derivation of Fundamental Physical Constants from Non-Well-Founded Set Theory

Current physical models rely on approximately 26 arbitrary fundamental constants (e.g., mass of proton, fine structure constant). This paper proposes the Topographical Subset Ontology (TSO), a framework that derives these constants as emergent properties of a recursive logical system satisfying the Anti-Foundation Axiom (AFA). By defining "Physical Action" as the computational cost of self-verification (Principle of Least Structural Action), we derive a "Logical Boltzmann Constant" ($k_L = \hbar \ln 2$) and calculate the structural complexity of the proton as $v \approx 9.06$. We demonstrate that Mass is recursive depth, Charge is topological instability, and Dark Matter consists of closed recursive loops. Finally, we propose a novel experimental test: detecting a "Resonance Dip" in the Hydrogen hyperfine line at 242.6 MHz, predicted as the frequency required to stabilize the proton’s topological leak.