Gauge Field Theory within the Cognitive Phase Space Framework: An Information-Geometric Explanation of the Yang-Mills Equations

The Yang-Mills gauge field theory serves as the core mathematical framework of the Standard Model of particle physics. However, the selection of the gauge group SU(3)×SU(2)×U(1) lacks a first-principles criterion for its preference, and the Higgs mechanism cannot explain the underlying constraint logic behind spontaneous symmetry breaking and the mass gap. Based on the axiomatic system of the Origin of Curiosity theory and the cognitive phase space mathematical framework, this paper introduces the principle of cognitive information-geometric optimization, establishing an effective action framework that couples cognitive constraints with gauge field theory. Based on the three foundational constraints of cognitive systems, a gauge group selection criterion is proposed, demonstrating that SU(3)×SU(2)×U(1) is the minimal, lowest information-encoding-cost gauge group combination that satisfies all constraints. Relying on this coupling framework, a cognitive information-geometric explanation of spontaneous symmetry breaking and the mass gap is provided, along with falsifiable experimental observational predictions. This work establishes a unified paradigm for dialogue between cognitive evolutionary axioms and microscopic gauge field theory, providing a novel research direction for tracing the underlying parameters of the Standard Model.