Preliminary Abstract
The Yang–Mills mass gap problem concerns why gauge fields exhibit a strictly positive energy gap despite the absence of explicit mass terms in the underlying equations. Conventional approaches have primarily investigated this phenomenon through quantum field theory, spectral analysis, and non-perturbative gauge dynamics. Although remarkable progress has been achieved, the origin of the mass gap continues to suggest that stable gauge configurations may be governed by structural principles extending beyond purely temporal or perturbative formulations.
In this work, we examine the Yang–Mills problem through the Changbal Jump Machine (CJM), interpreting gauge-field organization within the atemporal complexity class O(J). Rather than viewing mass as a quantity generated through temporal dynamical evolution, the proposed framework regards mass as an intrinsic property of structurally admissible gauge configurations. The emphasis therefore shifts from temporal generation to atemporal structural organization.
Within this perspective, the Yang–Mills mass gap is interpreted as the essential energy separation between stable gauge configurations. CJM views this separation as the consequence of the lowest resonant mode permitted by gauge invariance, where discrete phase-locked gauge states form structurally coherent configurations. Mass consequently appears as an atemporal property of resonantly organized gauge fields rather than as a quantity accumulated through temporal evolution.
Building upon these ideas, we introduce CJM–Yang, a structural resonance framework for analyzing phase-locked Yang–Mills gauge states. The proposed formulation interprets the Yang–Mills mass gap through resonantly organized gauge configurations while preserving the common Universal CJM Core Engine developed throughout the Unified Field series. Beyond this physical interpretation, the same formulation may, when appropriate, be applied as an additional resonance-based perspective for examining the structural consistency of CJM outcomes.
From this perspective, the physical realization of mass reflects the existence of discrete, resonantly stable gauge configurations that remain structurally coherent independently of temporal evolution. Accordingly, the Yang–Mills formulation is not introduced as a mandatory stage of the CJM framework, but as an optional interpretive filter that may provide complementary structural evidence alongside other available analyses. Its purpose is to enrich the interpretation of CJM results rather than to determine, modify, or replace the primary structural judgment.
No formal proof of the Yang–Mills existence and mass gap problem is claimed. Instead, this paper presents a CJM-based structural reformulation in which gauge fields, mass generation, and energy separation are interpreted through structural resonance, phase-locked configurations, and atemporal organization. By extending the Unified Field series from mathematical reformulation toward multi-filter structural verification, the proposed Yang–Mills framework establishes a complementary physical validation mechanism within the broader CJM architecture.
Keywords: Atemporal Computation; Changbal Jump Machine (CJM); O(J); Navier-Stokes equations; NS equation; Trinity Resonance; P vs NP; NP Problem; Time Crystal; allthingsareP; 창발
The Master Manifesto. We propose a shift in addressing the Millennium Prize Problems from exclusively formal, time-bound proof toward structural and physically discriminable experimentation, reinterpreting mathematical conjectures not as statements requiring asymptotic derivation but as questions of realizability within a structured, non-temporal state space.
This series originates from the P versus NP problem, reformulated through the Changbal Atemporal Equation, P ≡ NP\(^{J}\), and evaluated by the Changbal Jump Machine (CJM). The term Changbal is derived from the Korean conceptual notion of 창발 and denotes a discontinuous structural transition beyond constraint boundaries, distinct from gradual emergence; within this framework, solvability is defined by structural admissibility rather than computational effort.
The technical foundations of the O(J) state space, the Changbal Atemporal Equation, and the CJM architecture have been developed and analyzed in detail in prior work [?]; accordingly, these elements are treated here as established primitives, and the present paper focuses exclusively on their application to a specific conjecture rather than on re-deriving or extending the underlying formalism.