Valuation Axiom, Uncertainty Principle, and Fault-Tolerance Axiom: The Triple Core Logic of Universal Self-Stability and Irreversible Protection

This paper constitutes the tenth formal study within the Pythagorean Frustum Unified Research Consortium (PFUSRC) theoretical system. Based on the 45° coaxial double-cone topology and universal closed dynamics, a complete axiomatic framework is established, including the universal philosophical axiom, the irreversible invariant formula, the valuation axiom, the generalized uncertainty principle, and the fault-tolerance axiom. The valuation axiom defines the ontological interval property of local