The Seonggil-Dirac-Einstein Unified Field Theory: Non-commutative Chern-Simons Invariant and the Algebraic Resolution of the Information Paradox

This paper presents the Seonggil-Dirac-Einstein (SDE) unified field theory, grounded in the framework of Rough Operator Algebra (ROA) and Seonggil Hypercomplex numbers (ˆiR). By redefining the spacetime volume element as a non-commutative commutator space, we derive a dynamic mechanism for the time-varying dark energy (Quintessence) perfectly matching DESI observational data without resorting to ad-hoc scalar fields. Furthermore, we establish the Seonggil Non-commutative Chern-Simons invariant (ISCCS), which provides a geometric topological sieve that naturally generates matter-antimatter asymmetry (Baryo genesis) during the reheating phase. Ultimately, we prove that the black hole information paradox is an illusion of classical geometry; physical information is holographically encoded into algebraic solitons via the trace of the Moyal-Weyl star product (Tr⋆^(ROA) )algebraic reversibility and information conservation.