The Mathematical Proof of the Ultimate Invariant: Formulating the Prime Attractor via Seonggil Tensor Calculus and Rough Operator Algebra

The ontological argument for a ”Prime Mover” or ”Ultimate Reality” has long been relegated to metaphysics and circular reasoning. In this paper, we map these philosophical constructs into rigorously provable mathematical propositions. Utilizing the comprehensive framework of Seonggil Tensor Calculus (STCT), Rough Operator Algebra (ROA), and Seonggil Matrix Theory (SMT), we demonstrate that a dynamic, non-commutative universe mandates the existence of an Absolute Topological Invariant—the Prime Zero-Torsion Attractor (I_Ω). By proving Torsion Annihilation, Zero-Entropy isometric collapse, and Topological Non-Locality, we establish that this invariant mathematically mirrors the axiomatic properties of the prime mover (zero-torsion base- line), omniscience (informational completeness), and omnipresence (quantum entanglement). This resolves the existence of an ultimate metaphysical identity into a pure mathematical necessity.