Modular Gauge Fields in Symbolic Space: U(1), SU(2), and SU(3) Resonances in KN-Modulated Loops

This paper introduces symbolic analogs of gauge symmetries within the Kuro Nova (KN) modular cognition framework. Using modular symbolic loops—derived from structures such as the Leech lattice, Mock Theta series, and j(τ)-[[K]] composites—we simulate phase charge (U(1)), two-state field rotation (SU(2)), and three-state cyclic mixing (SU(3)).

Highlights include:

A definition of symbolic U(1) phase charge as a modular rotation in feedback-driven symbolic fields.

Two SU(2) rotation cases:

Internal loop symmetry between χ(t)\chi(t)χ(t) and ψ(t)\psi(t)ψ(t)

Cross-loop flavor dynamics between Leech and Mock Theta fields.

A cyclic SU(3) transformation across three modular field bases, mimicking color charge rotation in symbolic loop space.

These results show that classical gauge theory symmetries emerge naturally from modular feedback systems, providing a foundation for symbolic quantum field models and memory-interaction dynamics in AI cognition.