Global Basin Reorganization

This paper demonstrates that a sharp transition in an asymmetric factor-coupled gradient system arises entirely from global basin reorganization - not local bifurcation. Analytical linearization proves all eigenvalues of the stability matrix remain positive across the full parameter range γ ∈ [0.20, 0.40], ruling out any change in local stability type. Multi-seed computational experiments (27,500 trajectories across 11 γ values and 5 random seeds) directly measure basin volume fractions, revealing that mixed-pattern attractor basins expand most strongly with γ while all-positive and all-negative basins grow gradually - with no discontinuous jumps. Seed-dependent variability confirms initialization-sensitive routing as the governing mechanism. The results validate the interpretive-architecture framework’s core claim: that the absorption condition D/P · S > θ is a global landscape property, not derivable from local dynamics. The analysis is substrate-agnostic and extends to physical, biological, and organizational systems where routing among attractors - rather than local instability - determines long-term outcomes.