Stratified Formalization of a Relaxation-Oscillatory Phase-Portrait System

The framework begins with a single paradox: Absolute nothingness cannot stably remain nothingness. To define or maintain a void already introduces distinction, thereby negating pure void itself. Thus, the void is not a stable equilibrium but an unstable condition. Mathematically, the void corresponds to X=0X=0X=0. However, this state becomes unstable below a critical threshold, forcing the spontaneous emergence of an active state X>0X>0X>0. This is the first negation. The active state then generates its own background field: X↑⇒Y↑X↑ ⇒ Y↑⇒Y↑ Existence inevitably creates relations, structure, and context. Yet this generated background eventually destroys the very state that produced it. When the critical limit is reached, the active state collapses: Y→Ymax⇒X→0Y → Yₘₐₓ ⇒ X → 0Y→Ymax⇒X→0 This is the second negation. However, the system never returns to the original void. The history encoded in the background field remains. Consequently, the contradiction cannot be resolved by a fixed state and instead becomes a perpetual limit cycle: ω(Z)=Γω(Z)=Γω(Z)=Γ Existence is therefore not a static substance but a recurring process generated by the self-negation of nothingness. Prime structures (irreducibility), quantum entanglement (relationality), and the limit cycle (non-settlement) are not mathematically identical, but they exhibit a common abstract form: stable existence is impossible, and persistence emerges only through dynamic organization.