Information Dynamics: Emergence of Non-Abelian Gauge Fields from Local SU(N) Invariance of a Generalized Ginzburg--Landau Equation and Phenomenological Consistency with Four Independent Experiments

This paper extends the Information Dynamics framework to non-Abelian gauge fields. The information field is generalized to a multi-component complex vector. Requiring local SU(N) invariance of the generalized Ginzburg-Landau equation naturally yields the Yang-Mills Lagrangian and the non-Abelian field strength tensor. The only control parameter is the information purity p_ID, which determines the coherence scale and the masses of gauge bosons. We extract p_ID from four independent experiments using publicly available data: hyperon semileptonic decay (BESIII 2021), reactor neutrino oscillation (KamLAND and JUNO 2025), the X17 resonance (Atomki 2020), and the muon g-2 anomaly (Fermilab 2025). All four extractions give p_ID close to 1, indicating that the underlying information field resides in an information-superconducting state. Strong and weak interactions thus emerge as internal rotational symmetries of the information field. The Value of Information Dynamics: A New Perspective, Not Just New Predictions Information Dynamics is not intended to replace or overturn the Standard Model at currently accessible energy scales. Its role is analogous to that of a high‑level programming language—the binary code compiled from a high‑level language may be functionally identical to hand‑written assembly, yet the value of the high‑level language lies in simpler abstractions, greater unifying power, and the ability to solve complex problems. Similarly, starting solely from binary code, there are several ways to prove the existence of a high‑level programming language (e.g., bootstrapping, cross‑platform consistency, solving problems impractical in binary, information compression, extensibility, etc.). However, each of these approaches requires substantial time and broad collaboration. This paper serves only as the beginning of such an ambitious endeavor, presenting the core ideas and initial constructions. This paper takes only the first step—demonstrating the basic syntax and core ideas of Information Dynamics as a “high‑level language.” We sincerely invite colleagues in the academic community to collaborate and together complete this grand bootstrapping project. Upload note: All data are taken from published literature. The Python code for the extractions is available on GitHub https://github.com/hkaiopen/InformationDynamics_particlephysics/.