PFUSRC-108 Topological One-Loop Correction of Vacuum Polarization and Topological Anchoring of the QED Fine-Structure Constant Supplementary Supporting Manuscript for PFUSRC-107 Topological Flow-Variable Evolution Tensor Framework

This paper adopts the 11-dimensional topological flow-variable evolution tensor strictly defined in PFUSRC-107 as the exclusive deduction tool, and completes the high-dimensional topological ontological reinterpretation of full radiative corrections in Quantum Electrodynamics (QED). Four core physical puzzles are systematically resolved: topological self-consistent correction for one-loop Feynman diagrams of vacuum polarization, the geometric projection origin of the fine-structure constant ≈1 / 137 under the triple coaxial bicone structure, the quantitative topological symmetry-breaking expression of the electron anomalous magnetic moment (g-2 factor), and the hydrogen Lamb shift energy-level splitting mechanism triggered by topological boundary locking of topological flow variables (TFVs). Within the core steady-state paradigm of PFUSRC, vacuum is not the empty background defined in classical physics, but a globally continuous superposition field of uncondensed four-dimensional Topological Flow Variables (TFVs). Conventional closed virtual-particle loop diagrams in QED essentially represent homotopic closed winding trajectories formed by TFVs on the inner concave surface of the bicone manifold, and the winding number of each loop is quantized and constrained by the intrinsic Z₃ triple coaxial cyclic symmetry group of the system. The inherent ultraviolet divergence arising from the vacuum polarization integral in standard quantum field theory is identified as an incompleteness defect caused by artificially truncating the 11-dimensional manifold curvature boundary term R^ (M₁₁ ₃) within low-dimensional effective equations. After embedding the topological critical locking threshold ₂ₑ₈ₓ derived from PFUSRC-107, intrinsic topological regularization is realized via high-dimensional geometric boundary constraints, avoiding reliance on heuristic mathematical regularization remedies such as artificial momentum cutoff and dimensional analytic continuation. This paper further demonstrates that the fine-structure constant is not a fundamental free parameter of the universe, but a dimensionless geometric projection coefficient generated by orthogonally projecting the 45° half-apical-angle triple coaxial nested bicone structure onto the three-dimensional observable subspace, topologically constrained and uniquely fixed by Z₃ triple-fold symmetry. The minute measurable deviation between the theoretical geometric value and experimental data originates from weak continuous topological symmetry breaking of the global 11-dimensional mother topological manifold. Together with the drift of the dynamically effective Planck constant h₄₅₅ and the ₁ rhythmic dynamic constant proposed in PFUSRC-097, a complete closed loop for dynamic constant evolution is constructed. The slight departure of the electron g-factor from the ideal value of 2, as well as the hydrogen Lamb energy-level splitting, can both be quantitatively attributed to local weak torsional breaking perturbations of the ideal bicone steady-state configuration. All correction terms strictly comply with the tensor symmetry rules, dominant positive-definite energy conditions and topological parity-breaking criteria formulated in PFUSRC-107. This manuscript finalizes the quantitative verification chain of the PFUSRC topological unified system spanning from high-dimensional geometric axioms to low-energy QED experimentally measurable observables, and achieves underlying logical unification between topological ontology and microscopic quantum measurable effects.