The topological phase (x)\theta(x) can arise from several sources:
Berry phase accumulated via adiabatic transport of a quantum state across varying spacetime geometries,
Chern-Simons-type terms induced by topological field theory,
Path integral winding contributions from multi-connected spacetimes.
In the layered universe framework, we model:
(x)=ii(x)i\theta(x) = \sum_i \chi_i(x) \theta_i
where:
i(x)[0,1]\chi_i(x) \in [0,1] is a layer participation function, denoting how strongly point xx is influenced by layer ii,
i\theta_i is the global phase angle associated with layer ii, which may encode intrinsic curvature, torsion, or quantum coherence properties of that layer.
2. Physical Interpretation
The exponential exp(i(x))\exp(i\theta(x)) acts analogously to a quantum wavefunction amplitude in a topologically complex spacetime. When summed or integrated across domains, constructive and destructive interference patterns emerge depending on relative phase differences between layers.
