Persistence of Hierarchical Structure Under Random Seeding

We test the persistence of hierarchical heavy-tailed structure under randomized seeding. All system parameters and acceptance criteria are held fixed, and only the random seed is varied across independent realizations. Using an unchanged multi-metric gate, we find that a substantial fraction of runs satisfy the acceptance criteria, indicating that the regime is not a single-seed artifact but a structurally stable phase of the system. Across 100 independent seeds, approximately 51% satisfy all structural criteria.