Quantitative Operational Standards for Existence and Stability Criteria in Layered τ₀ Theory

We present a systematic, first-principles derivation of quantitative operational standards for the Existence Criterion (EC) and Stability Criterion (SC) within the Layered τ₀ Theory framework. By defining the ratio and applying a reductio ad absurdum approach, we demonstrate that all physically realizable systems naturally exhibit a monotonic saturating response in this ratio. This work establishes a rigorous mathematical and physical foundation for quantifying system stability and existence without relying on experimental datasets, using only fundamental physical constants, characteristic timescales (e.g., quantum coherence, decay lifetimes), and logical constraints.