A Unified Framework of Quantum Gravity and Macroscopic Spacetime via Universal Rough Operator Algebra (UROA), Hypertensor Mechanics, and Seonggil Field Equations (SFE): An Observational and Phenomenological Synthesis

Abstract

To resolve the ultraviolet (UV) divergence and singularity problems that prevent the unification of general relativity and quantum field theory (QFT), this study re-defines spacetime as a non-commutative Rough Operator Algebra (ROA) space A_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. By introducing the topological source term J^topo_µν (α,φ) and the Seonggil Field Equations (SFE), we successfully control the infinite divergence of quantum vacuum fluctuations without artificialrenormalization. Crucially, this upgraded framework derives explicit quantitative predictions for the residual torsion anomaly, phenomenologically maps the G_2 gauge associator to the running coupling of the Standard Model, and provides a mathematically reproducible toy model for scattering amplitudes using fractional calculus.