A Unified Framework of Quantum Gravity and Macroscopic Spacetime via Universal Rough Operator Algebra (UROA), Hypertensor Mechanics, 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) spaceA_α governed by infinite-dimensional Hypertensor mechanics. 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 g_µν 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 ˆT_res replaces gravitational effects. By integrating the G_2 gauge associator and continuous dynamic rankcalculus, the Seonggil Field Equation (SFE) naturally derives standard model symmetries without ad-hoc insertions. Furthermore, through the sweeping data of the dynamic behavior of an advanced number-theoretic algorithm (V85 Asymmetric Engine), we present empirical evidence of the absolute isomorphism between continuous algebraic topological space, fractional information recovery, and physical quantum gravitational space.