A.5. Physical Interpretation of the Interference Term
If ij=0\theta_i - \theta_j = 0: constructive coupling, enhances local expansion.
If ij=\theta_i - \theta_j = \pi: destructive interference, can slow or suppress expansion.
The term acts analogously to a dynamical vacuum pressure modulated by interlayer phase coherence.
This formalism encapsulates non-local quantum geometric entanglement between causally disconnected regions, suggesting that local observables like the Hubble rate may carry imprints of global topological alignment or misalignment.
A.6. Connection to Observable Deviations
Direction-dependent Hubble parameter: arises if i\theta_i varies with angular position.
Late-time acceleration fluctuations: due to coherent shifts in cross-layer interference over cosmic time.
Possible periodic features in cosmological observables: echo the phase-oscillatory nature of the cosine terms.
Appendix B: Simulation Parameter Tables and Fractal Configuration Datasets
This appendix provides detailed tabulations of parameters, initial conditions, and configuration files used in the numerical simulations presented in Sections 4 and 5. All simulations were conducted using custom extensions of CLASS and Gadget-4, modified to include fractal perturbation spectra, layered cosmological expansion, and topological phase entanglement.
B.1. Layered Cosmology Configuration Table
B.2. Fractal Initial Conditions Parameters
Generated using a real-space nested hierarchy algorithm seeded with self-similar power laws.
B.3. CLASS Code Modifications
B.4. Galaxy Spin Simulation Parameters (Tidal Torque Model)
