Absolute Resolution of Kaplansky's Conjecture: Topological Rigidity via Vanishing Seonggil Torsion Tensors

Kaplansky’s Unit Conjecture, positing that the unit group of a group algebra K[G] over a torsion-free group G consists only of trivial units, has long remained an open challenge in non-commutative algebra. This paper resolves the conjecture by reinterpreting the unit structure as a topological loop within the framework of Rough Operator Algebra (ROA).We demonstrate that the algebraic ”torsion-free” condition is geometrically equivalent to a vanishing Seonggil Torsion Tensor (T_STCT ≡ 0). By invoking the Rigidity Equation governed by the Seonggil Field Equations (SFE), we rigorously prove the absolute topological rigidity of the group algebra, thereby precluding the formation of non-trivial units.