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التفاصيل البيبلوغرافية
المؤلف الرئيسي:	Maley, Amos Jay
التنسيق:	Recurso digital
اللغة:
منشور في:	Zenodo 2026
الموضوعات:	Yang-Mills theory mass gap quantum field theory constructive field theory lattice gauge theory mathematical physics Wilson action Osterwalder-Schrader reconstruction Wightman axioms
الوصول للمادة أونلاين:	https://doi.org/10.5281/zenodo.19640681
الوسوم:	إضافة وسم لا توجد وسوم, كن أول من يضع وسما على هذه التسجيلة!

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<h2>Description</h2> This work presents a theorem establishing a vacuum-sector mass gap for the bounded-region local gauge-invariant sharp-local Yang–Mills net associated to any compact connected simple gauge group GGG. The proof is organized through a finite packet reduction architecture consisting of: <ul> <li>a compact-simple ultraviolet gate,</li> <li>a Route 1 lattice-to-continuum vacuum-gap chain,</li> <li>a Lane A sharp-local constructive chain,</li> <li>and a theorem-level endpoint packet (OS/Wightman reconstruction and local-net identification).</li> </ul> The theorem-level object is explicitly local: the result applies to the bounded-region gauge-invariant sharp-local net generated by flowed curvature composites. Extended-support line and surface sectors are excluded from the theorem claim. <h2>Formal Verification Layer</h2> The manuscript is accompanied by a Lean4 formal verification layer that certifies the theorem-level dependency structure and closure architecture. <ul> <li>The Lean development verifies: <ul> <li>packet routing and reduction,</li> <li>dependency DAG and theorem ownership,</li> <li>closure interfaces across Route 1, Lane A, and endpoint assembly,</li> <li>non-circularity of the proof spine,</li> <li>consistency between manuscript claims and proof structure.</li> </ul> </li> <li>The Lean layer operates relative to an explicitly declared imported substrate: <ul> <li>standard Wilson lattice Yang–Mills theory,</li> <li>standard Osterwalder–Schrader reconstruction framework.</li> </ul> </li> </ul> Formalization of this standard substrate is outside the scope of the present verification layer. <h2>Main Result (informal summary)</h2> The constructed sharp-local Yang–Mills theory satisfies: <ul> <li>existence of a continuum local gauge-invariant quantum field theory,</li> <li>OS/Wightman reconstruction,</li> <li>Haag–Kastler local net structure,</li> <li>non-triviality (nonzero spectral weight),</li> <li>and a strictly positive vacuum mass gap:</li> </ul> Spec(H)⊂{0}∪[m&lowast;,∞),m&lowast;>0.\mathrm{Spec}(H) \subset \{0\} \cup [m^*, \infty), \quad m^* > 0.Spec(H)⊂{0}∪[m&lowast;,∞),m&lowast;>0. The continuum local theory is faithful-Wilson universal at theorem level: all faithful ultraviolet Wilson regularizations of the same group GGG yield canonically isomorphic local theories (qualitatively). Explicit quantitative bounds remain indexed by the chosen ultraviolet regularization. <h2>Scope Clarifications</h2> This work does not claim: <ul> <li>a mass gap for nonlocal sectors (line/surface operators),</li> <li>uniform quantitative bounds across all faithful representations,</li> <li>formalization of the Wilson QFT substrate in Lean,</li> <li>results outside the admissible gradient-flow renormalization class.</li> </ul> <h2>Structure of the Archive</h2> The Zenodo record includes: <ul> <li>Core manuscript (theorem and proof spine)</li> <li>Companion I: ultraviolet gate and Route 1 chain</li> <li>Companion II: Lane A constructive chain</li> <li>Companion III: reconstruction and endpoint packet</li> <li>Lean4 verification layer (dependency and closure certification)</li> </ul> <h2>Significance</h2> The contribution is twofold: <ol> <li>A constructive Yang–Mills mass-gap proof framed at the level of local nets.</li> <li>A machine-verified proof architecture that eliminates hidden dependencies and enforces explicit theorem-level closure.</li> </ol>

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