Vacuum-sector mass gap for the local gauge-invariant sharp-local Yang–Mills net
Fuente:
Zenodo
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Recurso digital |
| Publié: |
Zenodo
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866902203186282496 |
|---|---|
| author | Maley, Amos Jay |
| author_facet | Maley, Amos Jay |
| contents | <h2>Description</h2> <p>This work presents a theorem establishing a <strong>vacuum-sector mass gap</strong> for the bounded-region local gauge-invariant sharp-local Yang–Mills net associated to any compact connected simple gauge group <span><span>GG</span><span><span><span>G</span></span></span></span>.</p> <p>The proof is organized through a finite <strong>packet reduction architecture</strong> consisting of:</p> <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> <p>The theorem-level object is explicitly <strong>local</strong>: 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.</p> <h2>Formal Verification Layer</h2> <p>The manuscript is accompanied by a <strong>Lean4 formal verification layer</strong> that certifies the theorem-level dependency structure and closure architecture.</p> <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 <strong>relative to an explicitly declared imported substrate</strong>: <ul> <li>standard Wilson lattice Yang–Mills theory,</li> <li>standard Osterwalder–Schrader reconstruction framework.</li> </ul> </li> </ul> <p>Formalization of this standard substrate is <strong>outside the scope</strong> of the present verification layer.</p> <h2>Main Result (informal summary)</h2> <p>The constructed sharp-local Yang–Mills theory satisfies:</p> <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> <p><span><span><span>Spec(H)⊂{0}∪[m∗,∞),m∗>0.\mathrm{Spec}(H) \subset \{0\} \cup [m^*, \infty), \quad m^* > 0.</span><span><span><span><span>Spec</span></span><span>(</span><span>H</span><span>)</span><span>⊂</span></span><span><span>{</span><span>0</span><span>}</span><span>∪</span></span><span><span>[</span><span><span>m</span><span><span><span><span><span><span>∗</span></span></span></span></span></span></span><span>,</span><span>∞</span><span>)</span><span>,</span><span><span>m</span><span><span><span><span><span><span>∗</span></span></span></span></span></span></span><span>></span></span><span><span>0.</span></span></span></span></span></p> <p>The continuum local theory is <strong>faithful-Wilson universal</strong> at theorem level: all faithful ultraviolet Wilson regularizations of the same group <span><span>GG</span><span><span><span>G</span></span></span></span> yield canonically isomorphic local theories (qualitatively).</p> <p>Explicit quantitative bounds remain indexed by the chosen ultraviolet regularization.</p> <h2>Scope Clarifications</h2> <p>This work does <strong>not</strong> claim:</p> <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> <p>The Zenodo record includes:</p> <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> <p>The contribution is twofold:</p> <ol> <li>A constructive Yang–Mills mass-gap proof framed at the level of local nets.</li> <li>A <strong>machine-verified proof architecture</strong> that eliminates hidden dependencies and enforces explicit theorem-level closure.</li> </ol> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19640681 |
| institution | Zenodo |
| language | |
| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | Vacuum-sector mass gap for the local gauge-invariant sharp-local Yang–Mills net Maley, Amos Jay Yang-Mills theory mass gap quantum field theory constructive field theory lattice gauge theory mathematical physics Wilson action Osterwalder-Schrader reconstruction Wightman axioms <h2>Description</h2> <p>This work presents a theorem establishing a <strong>vacuum-sector mass gap</strong> for the bounded-region local gauge-invariant sharp-local Yang–Mills net associated to any compact connected simple gauge group <span><span>GG</span><span><span><span>G</span></span></span></span>.</p> <p>The proof is organized through a finite <strong>packet reduction architecture</strong> consisting of:</p> <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> <p>The theorem-level object is explicitly <strong>local</strong>: 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.</p> <h2>Formal Verification Layer</h2> <p>The manuscript is accompanied by a <strong>Lean4 formal verification layer</strong> that certifies the theorem-level dependency structure and closure architecture.</p> <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 <strong>relative to an explicitly declared imported substrate</strong>: <ul> <li>standard Wilson lattice Yang–Mills theory,</li> <li>standard Osterwalder–Schrader reconstruction framework.</li> </ul> </li> </ul> <p>Formalization of this standard substrate is <strong>outside the scope</strong> of the present verification layer.</p> <h2>Main Result (informal summary)</h2> <p>The constructed sharp-local Yang–Mills theory satisfies:</p> <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> <p><span><span><span>Spec(H)⊂{0}∪[m∗,∞),m∗>0.\mathrm{Spec}(H) \subset \{0\} \cup [m^*, \infty), \quad m^* > 0.</span><span><span><span><span>Spec</span></span><span>(</span><span>H</span><span>)</span><span>⊂</span></span><span><span>{</span><span>0</span><span>}</span><span>∪</span></span><span><span>[</span><span><span>m</span><span><span><span><span><span><span>∗</span></span></span></span></span></span></span><span>,</span><span>∞</span><span>)</span><span>,</span><span><span>m</span><span><span><span><span><span><span>∗</span></span></span></span></span></span></span><span>></span></span><span><span>0.</span></span></span></span></span></p> <p>The continuum local theory is <strong>faithful-Wilson universal</strong> at theorem level: all faithful ultraviolet Wilson regularizations of the same group <span><span>GG</span><span><span><span>G</span></span></span></span> yield canonically isomorphic local theories (qualitatively).</p> <p>Explicit quantitative bounds remain indexed by the chosen ultraviolet regularization.</p> <h2>Scope Clarifications</h2> <p>This work does <strong>not</strong> claim:</p> <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> <p>The Zenodo record includes:</p> <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> <p>The contribution is twofold:</p> <ol> <li>A constructive Yang–Mills mass-gap proof framed at the level of local nets.</li> <li>A <strong>machine-verified proof architecture</strong> that eliminates hidden dependencies and enforces explicit theorem-level closure.</li> </ol> |
| title | Vacuum-sector mass gap for the local gauge-invariant sharp-local Yang–Mills net |
| topic | Yang-Mills theory mass gap quantum field theory constructive field theory lattice gauge theory mathematical physics Wilson action Osterwalder-Schrader reconstruction Wightman axioms |
| url | https://doi.org/10.5281/zenodo.19640681 |