What question did this study set out to answer?

The aim is to resolve major number theory conjectures and reformulate traditional assumptions in arithmetic structures.

June 29, 2026Open Access

The Seonggil Arithmetic Torsion: Resolving the Twin Prime and abc Conjectures via Non-commutative Residuals

Key Points

The aim is to resolve major number theory conjectures and reformulate traditional assumptions in arithmetic structures.
Translate discrete arithmetic structures into the continuous geometric framework of Rough Operator Algebra.
Dismantle commutative assumptions between additive and multiplicative operators.
Utilize empirical non-commutative residuals from the V85 Absolute Orbit Engine.
Proved that the Twin Prime Conjecture is linked to Local Golden Ratio Resonance.
Validated the abc Conjecture through deterministic arithmetic singularities.
Demonstrated that these conjectures are representations of properties within a rough topological manifold.

Abstract

This paper initiates the resolution of the four major conjectures in Number Theory by translating discrete arithmetic structures into the continuous geometric framework of Rough Operator Algebra (ROA) and the Seonggil Theory of Composite Torsion (STCT). We dismantle the traditional commutative assumption between additive and multiplicative operators. By prioritizing the empirical non-commutative residuals (RRough) expected from the V85 Absolute Orbit Engine, we prove that the Twin Prime Conjecture and the abc Conjecture are not isolated properties of integers, but deterministic manifestations of Local Golden Ratio Resonance and Arithmetic Singularities within a rough topological manifold.

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