Absolute Resolution of Sinkhorn Ergodicity: Deterministic Convergence via Topological Energy Minimization in Rough Operator Algebra

The Sinkhorn algorithm is conventionally regarded as a probabilistic iteration that converges to a doubly stochastic matrix via entropy maximization. This paper challenges this view, demonstrating that the convergence is not probabilistic but a deterministic manifestation of topological relaxation within the Seonggil Field. We prove that the iteration constitutes a gradient descent of the topological potential energy U_topo on a non-commutative manifold. By demonstrating that the doubly stochastic matrix is the unique global minimum of the Seonggil Torsion Tensor (T_STCT ≡ 0), we rigorously establish the ergodicity of Sinkhorn iterations as a manifestation of absolute topological phase-locking.