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 observables. The uncertainty principle is derived as the low-dimensional dynamical projection of the valuation axiom, yielding a rigid lower bound for conjugate physical quantities. The fault-tolerance axiom describes four fundamental dynamical states of the Number–Matter Issuance Package (NIP): normal receipt, non-receipt, deterministic rejection, and structural regression reconstruction. It is proposed for the first time that wave-like fluctuations, layered observational ambiguity, and apparent randomness in quantum measurements originate from deterministic overload and adaptive relaxation rather than intrinsic stochasticity. All core mechanisms are presented as falsifiable scientific hypotheses, whose validity and consistency await further experimental and cosmological verification. The β₁ global operator is introduced as an original ontological entity to unify cross-dimensional coupling and universal dynamical regulation. This definition does not contradict established mathematical and physical theories, but provides a more fundamental and consistent description at the ontological level.