The Principle of Existence Cost: Minimum Conditions for Stable Existence with MPCT as Minimal Realization

This paper introduces and formally establishes the Principle of Existence Cost(PEC): stable existence of any physical structure requires continuous non-zero energy expenditure. Through extensive numerical experiments (50,000 random configurations) based on the Minimal Phase Closure Triangle (MPCT) model, we demonstrate that stable closures constitute only 0.86% of possible configurations, andcrucially, none exhibit zero energy output. The minimum existence cost Φminrepresents a fundamental lower bound for stable being.out > 0The PEC states: (1) Stable existence corresponds to minimal closed structures;(2) Such structures must be in continuous dynamic oscillation; (3) Zero-cost existence is statistically impossible. The MPCT model serves as the minimal geometric realization of PEC, requiring three irreducible residuals (∆r, ∆θ, ∆τ) whosequadratic synergy maintains closure.Numerical results show: ⟨Φminout ⟩ = 0.093, minimum = 6.60 × 10−3, maximum=0.517, with strict positivity verified by statistical tests (p < 10−300). This providesa unified explanation for quantum zero-point fluctuations, particle spin, and vacuuminstability as manifestations of existence cost payment.Keywords: Existence Cost Principle, MPCT, Minimal Closure, Non-Zero Output, Stable Existence, Dynamic Oscillation