Lee Seonggil

Non-commutative Electrodynamics on Rough Manifolds: The Fusion of Maxwellian Equations and Hypercomplex Gauss Integrals

Traditional Maxwellian electrodynamics relies on the commutativity of spacetime coordinates, inherently failing to account for the intrinsic roughness of the manifold at the Planck scale. Modern extensions, such as Born-Infeld non-linear electrodynamics and premetric formalisms,...

The Absolute Spectral Resolution of the Birch and Swinnerton-Dyer Conjecture: Fractional Néron-Tate Pairing and ROA Fractal Brake

The Birch and Swinnerton-Dyer (BSD) Conjecture has remained unresolved primarily due to the structural chasm between the analytic rank of the Hasse-Weil L-function and the algebraic rank of elliptic curves, particularly for rank >= 2 where explicit geometric cycle constructions f...

The Absolute Resolution of the Yang-Mills Mass Gap: Rough Operator Algebra, Osterwalder-Schrader Reconstruction, and Arithmetic Friction

The Yang-Mills Existence and Mass Gap problem demands not only the demonstration of a strictly positive mass gap (∆ > 0) but also the rigorous construction of a non-trivial quantum gauge theory satisfying the Osterwalder-Schrader (OS) axioms in the continuum limit. This paper pro...

A Unified Framework of Quantum Gravity and Macroscopic Spacetime via Universal Rough Operator Algebra (UROA), Hypertensor Mechanics, and Seonggil Field Equations (SFE): An Observational and Phenomenological Synthesis

To resolve the ultraviolet (UV) divergence and singularity problems that prevent the unification of general relativity and quantum field theory (QFT), this study re-defines spacetime as a non-commutative Rough Operator Algebra (ROA) space A_α governed by infinite dimensional Hype...