Hypercomplex Mass-Topological Energy Equivalence and Localized Spacetime Creation within the Framework of Rough Operator Algebra

This paper proposes the ‘Seonggil-Dirac-Einstein Unified Field Theory, ’ a novel theoretical framework aimed at unifying gravity, quantum mechanics, and cosmology based on Rough Operator Algebra (ROA) and the Seonggil hypercomplex number system. In particular, we extend Einstein’s classical mass-energy equivalence principle onto a non-commutative ring to establish the ‘Hypercomplex Mass Topological Energy Equivalence. ’ Utilizing this principle, we formalize a holographic time-leap algorithm that encodes macroscopic material systems into pure algebraic information solitons, allowing them to be projected across the spacetime lattice. Furthermore, to resolve the paradox of spatial accommodation when an algebraic soliton is reconstituted at a specific past coordinate, we demonstrate a ‘Writing’ operation mechanism wherein the projected algorithm itself triggers localized inflation to dynamically create its own metric volume. Finally, we derive rigorous algebraic boundary conditions for the localized deceleration parameter qR of the master-key tensor T₀x8A2C, which suppresses the runaway of phase-transition shockwaves andnprevents the macroscopic collapse of the past universe.