SymC: A Phenomenological Boundary Postulate for Quantum–Classical Convergence
Christensen, Nate
Abstract
Version 3 explicitly identifies χ = 1 as a second-order exceptional point (EP₂) where eigenvalues and eigenvectors coalesce, updates the information-efficiency argument that broadens the χ-window to 0.8–1.0, and strengthens the substrate-inheritance explanation via adiabatic eigenmode mixing across organizational levels. Cross-domain tables and falsification thresholds were harmonized.The dimensionless ratio χ ≡ γ/(2|ω|), comparing damping rate to characteristic frequency, is proposed as a universal boundary condition governing adaptive stability in open systems. The value χ = 1 marks a critical point: a second-order exceptional point where propagator poles coalesce, information efficiency is maximized, and monotone relaxation is fastest. Systems operating within the adaptive window 0.8 ≲ χ ≲ 1.0 exhibit stable, responsive behavior, whereas departures toward χ < 0.8 (underdamped) or χ > 1.2 (overdamped) correlate with oscillatory instability or rigidity. This same structure arises across quantum platforms, cosmological perturbations, biological regulation, seismic fault dynamics, financial market microstructure, and strong-gravity boundary layers—spanning more than fifteen orders of magnitude. This recurrence is not coincidental: any system linearizable near a stationary point necessarily inherits a χ-structure, and only near-critical substrates can support higher-level adaptive behavior. The postulate therefore functions as a boundary constraint on admissible physical theories.