3. Topological Interpretation and Layer Interference
Each layer in the Multilayer Universe can be topologically characterized by a 3-manifold class Mi\mathcal{M}_i, whose connectivity is defined not by smooth coordinate overlap, but by a discrete adjacency matrix Tij{0,1}T_{ij} \in \{0,1\} governing allowed transitions or couplings.
This leads to an emergent topological spacetime graph, where:
Nodes represent universe layers Li\mathcal{L}_i,
Edges represent possible tunneling, causal, or phase coherence links.
Field configurations on this graph evolve according to a layered field equation:
ii+jTijF(ji)=Vii\Box_i \phi_i + \sum_j T_{ij} \mathcal{F}(\phi_j - \phi_i) = \frac{\partial V_i}{\partial \phi_i}
Where F\mathcal{F} is a coupling function (possibly sinusoidal for phase interference), and Vi(i)V_i(\phi_i) is the local potential.
This structure supports coherent oscillations, entropic gradients, or diffusion-like information exchange between layers, which may manifest observationally as:
Directional Hubble gradients,
Layer-specific void alignment patterns,
Phase-dependent lensing distortions.
4. Physical Interpretation: Void-Sheet Cosmology
Observationally, these layers may correspond to large-scale voids, walls, and filaments, seen as different "sheets" in the cosmic web---each with slightly different Hubble flow, galaxy clustering strength, and lensing signal.
In particular:
Gigaparsec-scale voids may mark transition zones between layers.
CMB dipole anomalies and quadrupole--octupole alignments may reflect projection effects from the underlying topological architecture.
5. Boundary Conditions and Metric Matching
