Unified Mathematical Definition of ``Self'': Causal Manifold, Observer, and Self-Referential Scattering Network

Within the framework of unified time scale, causal manifolds, and boundary time geometry, we provide an axiomatic mathematical definition of the first-person subject ``self''. The basic conception is: ``self'' is not a label for an instantaneous physical configuration, but rather an equivalence class of self-referential observer structures along a timelike worldline ordered by the unified time scale. At the geometric level, the universe is modeled as a globally hyperbolic Lorentzian manifold wit