Structural Isomorphism Between ``Self'' and ``Universe'': Unified Proof via Causal--Time--Entropy--Matrix Universe

Within framework of unified time scale, boundary time geometry, unified theory of causal structure, and self-referential scattering networks, this paper provides axiomatizable, theorem-provable mathematical version of proposition ``my mind is the universe'', giving rigorous proof of structural isomorphism between ``self'' and ``universe''. On one hand, based on Birman--Kreĭn formula and Wigner--Smith time-delay theory, we align total scattering half-phase derivative, spectral shift function, and