Asymptotic Limit Behavior of the ∆.72 Coherence Operator Under Infinite Oscillation and Full Harmonic Closure

This manuscript establishes the asymptotic limit behavior of the Δ72 Coherence Operator under joint limits of infinite oscillatory frequency (ω → ∞) and full harmonic closure (Φ_H → 1). Building on the contraction-based formulation introduced in earlier Δ72 coherence papers, we show that the operator’s effective convergence time T_{Δ72} collapses to zero in the continuous-time interpolation of the discrete dynamics, provided the contraction factor ρ(ω,Φ_H) satisfies a simple spectral decay model derived from strong convexity and smooth gradient flow. Theorem 4.1 formalizes this behavior, proving that the Δ72 operator acts as an instantaneous fixed-point contraction in the harmonic limit. Several figures illustrate the one-dimensional decay, geometric contraction, 2.5D joint-limit surface, and a full 3D vector field of trajectories approaching the attractor. This paper provides a mathematically consistent foundation for interpreting “instantaneous deterministic closure’’ in coherent physical, informational, and biological systems.