This abstract is made available here as a project-site research record. Following OpenAI's October 26, 2026 announcement of a proposed proof of Yang–Mills existence, we have chosen to temporarily defer public release of the full manuscript and submission to public preprint repositories and other archival channels, as the reported proof has not yet been publicly released for independent examination and while we reconsider its relationship to CJM–Yang.
CJM–Yang asks a different question: whether the existence of a positive mass gap can be discriminated through atemporal structural admissibility, without sequentially resolving gauge-field dynamics.
The abstract is preserved here in its present form to document the state of the research at this time. The full manuscript remains unpublished.
Please note that, as this is not the final published version, it may contain typographical or other errors.
The Yang–Mills existence and mass gap problem asks whether a nontrivial quantum Yang–Mills theory can be established in four-dimensional space and whether its physical spectrum possesses a strictly positive energy gap above the vacuum. Conventional approaches investigate this problem through quantum field theory, spectral analysis, lattice formulations, and non-perturbative gauge dynamics. Despite substantial progress, the mathematical origin of the mass gap remains unresolved.
We examine the Yang–Mills problem through the Changbal Jump Machine (CJM) and the atemporal complexity class O(J). This perspective does not remove time from gauge-field dynamics. Rather, it separates temporal evolution from structural discrimination and asks whether a positive mass gap can be understood as a property of structurally admissible gauge configurations. Gauge fields may evolve in time, while the admissibility of their organization remains a distinct structural question.
Within this framework, the mass gap is reinterpreted as a structural separation between the vacuum sector and the lowest admissible gauge-invariant excitation. Instead of viewing the gap only as an energy value obtained by resolving quantum dynamics, CJM asks whether the region immediately above the vacuum contains physically admissible gauge states. A positive mass gap is thus interpreted as a nonzero structural exclusion region separating the vacuum from the first admissible excitation.
We introduce CJM–Yang, a structural resonance formulation representing Yang–Mills gauge states through gauge-invariant constraints, phase coherence, spectral separation, and admissibility. The central question is whether the zero-gap limit remains structurally accessible or whether gauge-state organization enforces a strictly positive separation. Structural resonance represents global compatibility among gauge-field constraints, rather than asserting that conventional Yang–Mills theory contains the specific phase-locking mechanism proposed by CJM.
As a preliminary consistency test of structural discrimination, CJM–Yang considers finite-temperature SU(2) deconfinement, distinct from the zero-temperature mass-gap problem. The framework relates Polyakov-loop configurations to the fixed Universal CJM Core and defines an admissibility texture for comparison with three-dimensional Ising finite-size scaling. A single residual structural observable derived from this texture provides a basis for testing whether CJM captures measurable organization beyond known scaling contributions, with jackknife resampling for uncertainty estimation. This test does not itself establish a mass gap.
The primary role of CJM–Yang is to provide a structural interpretation of the Yang–Mills mass-gap problem. The gauge-resonance formulation also suggests a future role as a physical validation layer after the Universal CJM Core, where gauge coherence, spectral separation, and resonant stability could provide complementary evidence without replacing the primary TRUE/FALSE judgment. No formal proof of Yang–Mills existence or a positive mass gap is claimed; this work examines whether gauge invariance and spectral separation can be viewed through atemporal admissibility and structural resonance, and whether this reinterpretation reveals a measurable structural signature beyond conventional finite-size scaling. Extension to zero-temperature glueball correlators and the use of CJM–Yang as an internal physical validation mechanism remain future work.
Keywords: Atemporal Spectral Admissibility; Changbal Jump Machine (CJM); O(J); Yang–Mills; Mass Gap; Structural Resonance; Structural Admissibility; Gauge-Invariant States; 3SAT; 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≡NPᴶ, 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.