Unified Framework of Boundary Time--Topology--Scattering: From $\mathbb{Z

This paper constructs a unified framework centered on ``boundary time scale,'' gluing the following seemingly disparate structures into a single theory: (1) Local quantum sufficient conditions on small causal diamonds and nonlinear Einstein equations; (2) Z_2 holonomy in Null--Modular double covers and relative cohomology class [K] selected by BF bulk integration; (3) Family-level unification of restricted principal bundles--scattering--K^1 and the ``natural transformation unique up to integer m