A Discrete Informational Field Model for Emergent Gap Phenomena Inspired by Yang–Mills Theory
The existence of a mass gap in non-Abelian gauge theories remains one of the central open problems in mathematical physics. While traditional approaches rely on continuum formulations and functional analytic techniques, recent work has explored whether gap phenomena may arise from more fundamental discrete, geometric, or informational mechanisms. In this work, we introduce a minimal discrete informational–variational framework in which gap-like behavior emerges from purely local coherence constraints. A scalar informational coherence field defined on a finite lattice is analyzed through a differential coherence operator and a critical threshold condition, termed the Informational Gap Condition (IGC). Within this framework, persistent excitations arise exclusively as collective, super-threshold coherent structures, while subthreshold configurations decay under dissipative dynamics. We formalize this mechanism through structural lemmas governing coherence decay and cluster metastability, and we establish the emergence of a finite excitation gap in the thermodynamic limit. Crucially, the theoretical predictions are supported by numerical validation based on non-perturbative lattice simulations. The validation demonstrates the reconstruction of stable informational curvature structures, the appearance of a finite spectral gap, and scaling behavior consistent with established lattice Yang–Mills results, without the introduction of phenomenological mass terms or external tuning. The proposed model does not constitute a formulation of Yang–Mills theory. Rather, it provides a discrete informational analog that isolates a structural mechanism capable of generating gap phenomena, offering insight into the entropic and geometric foundations of mass emergence and collective stability in non-perturbative field theories. This work is situated within the broader conceptual framework of Viscous Time Theory (VTT), which interprets persistence and stability as emergent properties of informational coherence under local dissipation.
