A Unified Framework of Quantum Gravity and Macroscopic Spacetime via Universal Rough Operator Algebra (UROA) and Seonggil Field Equations (SFE)

To resolve the ultraviolet (UV) divergence and singularity problems that prevent the unification of general relativity and quantum field theory (QFT), this study redefines spacetime as a non-commutative ‘Rough Operator Algebra’ (ROA) space Aα. We demonstrate that the hypothetical graviton of mainstream physics is a perturbative ghost born from a categorical error. We mathematically prove that when the macroscopic spacetime metric gµν converges to a critical point αc of the roughness index α via an algebraic phase transition, the one-dimensional strings of superstring theory are reduced to topological defects, and the surviving residual torsion term ˆ Tres replaces gravitational effects. Furthermore, through the sweeping data of the dynamic behavior of an advanced number-theoretic algorithm (V85 Asymmetric Engine), we present empirical evidence of the isomorphism between algebraic topological space and physical quantum gravitational space.