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May 4, 2026Open Access

STCT-FOUNDATION Formal Axiomatization of Rough Operator Algebra and the Seonggil Field Equations via von Neumann Algebras

Key Points

The aim is to provide a rigorous mathematical framework for the Seonggil Theory of Composite Torsion and Rough Operator Algebra.
Mapped core axioms of STCT and ROA to von Neumann algebras.
Defined the Roughness Index as a semi-finite weight on a Type III1 factor.
Proven the topological dynamic evolution of spacetime via Tomita-Takesaki modular automorphism group.
Mapped the pure algebraic vacuum to the reference state (ω0).
Identified the Golden Ratio resonance frequency as a trigger for spacetime dynamics.
Established a foundation for concepts like macroscopic teleportation and interstellar traversal.

Abstract

This foundational paper establishes the rigorous mathematical framework for the Seonggil Theory of Composite Torsion (STCT) and Rough Operator Algebra (ROA) by mapping their core axioms to the standard language of von Neumann algebras. We define the fundamental ’Roughness Index’ (α) not merely as a geometric parameter, but as a faithful normal semi-finite weight on a Type III1 factor. The pure algebraic vacuum (α → 0) is mapped to the reference state (ω0), while the topological dynamic evolution of spacetime is formally proven to be governed by the Tomita-Takesaki modular automorphism group, directly triggered by the Golden Ratio resonance frequency (ωφ). This axiomatization provides the unassailable algebraic constitution underlying macroscopic teleportation, inertia-less flight, and interstellar traversal.

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