χ as a Transition Corridor Rather Than a Relaxation Attractor: Emergent χ-Corridor Formation in Recursive Coupling-Damping Systems

This work investigates the emergence of stable ratio corridors in recursive coupling-damping systems under asymmetric recursive evolution. The study focuses on the irrational stability ratio: χ ≈ 0.5512855984 Unlike previous recursive stability studies where χ was used as a direct stability target or regulator, this investigation intentionally excludes χ from the governing evolution equations. Instead, χ is applied only after simulation as a post-run measurement reference. A multi-seed computational sweep was performed using seven independent random seeds, with 20,000 recursive systems evolved per seed across a fine asymmetry sweep from 5.4 to 8.2 using step size 0.02. Despite χ being absent from the evolution dynamics, the simulations produced a persistent χ-near corridor satisfying: |C/K − χ| < 0.035 The corridor extended from asymmetry strength 5.82 through 8.20, with maximum χ occupancy reaching 100% near asymmetry strength 6.68. The closest mean-ratio agreement occurred at asymmetry strength 7.86, where the evolved systems produced: C/K = 0.5513233716 with absolute distance from χ: 3.78 × 10^-5 while maintaining complete system survival. The results suggest that χ behaves neither as ordinary equilibrium nor as a collapse boundary. Instead, the simulations support the interpretation of χ as a stable transition corridor embedded within a larger recursive branch manifold. This work does not claim direct physical proof of universality. Rather, it provides reproducible computational evidence for emergent χ-corridor formation under χ-blind recursive evolution.