The Geometry of Containment

The Geometry of Containment (3).pdf Through both stochastic and deterministic audits, the analysis demonstrates that previously assumed attractors fail under zero-baseline testing and that the observed system equilibrium converges toward the midpoint attractor M/2. A secondary observation reveals that these attractors consistently occur within containment intervals bounded by consecutive Fibonacci numbers across the tested modulus range. � � The paper introduces the concept of containment geometry, proposing that stability in constrained recurrence systems may arise from boundary relationships rather than equilibrium points alone. Within the tested recurrence class, Fibonacci-bounded containment intervals exhibit persistent alignment with Φ-proportional spacing, suggesting that the appearance of the Golden Ratio emerges from the structure of the recurrence system rather the Golden Ratio, nor does it assert that all systems converge to Φ. Instead, it documents an empirical observation within a defined class of modular recurrence systems and presents a falsifiable framework for future investigation into containment, recurrence, equilibrium, and constraint-driven stability. �