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Zenodo
2026
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| Accès en ligne: | https://doi.org/10.5281/zenodo.18519299 |
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- <p dir="ltr"> </p> <h1><a href="https://zenodo.org/records/18519299">ABSTRACT</a></h1> <p dir="ltr">Part XXVI continues the development of the Spectral Vacuum Mechanism (SVM), a Hamiltonian formulation of SU(3) Yang–Mills theory constructed across Parts XX–XXV. The earlier stages of the series established the mathematical and numerical foundations of the SVM: Parts XX–XXII introduced the truncated SU(3) Hamiltonian, the Gauss‑law operator, and the construction of the physical Hilbert space; Part XXIII produced the first complete low‑lying glueball spectrum; Part XXIV validated the continuum trajectory through a seven‑gate numerical audit; and Part XXV introduced the first fully gauge‑invariant observable layer, including Euclidean correlators, Wilson‑loop operators, and spectral susceptibilities.</p> <p dir="ltr">The present work addresses a conceptual and methodological question that remained unresolved in earlier parts of the series: Is the Wilson‑loop area law necessary to establish confinement in a Hamiltonian formulation of SU(3) gauge theory? We demonstrate that the answer is no. Confinement in the Hamiltonian SVM is established entirely through spectral diagnostics, while Wilson loops serve only as secondary infrared (IR) indicators.</p> <p dir="ltr">Building on the results of Part XXII and Part XXV, we show that the SVM Hamiltonian exhibits a stable mass gap of 1.68 ± 0.02 GeV (from the Hamiltonian spectrum), exponential decay of Euclidean correlators with a correlator‑based mass of 1.65 ± 0.05 GeV (from Part XXV), a finite correlation length of 0.12 fm, absence of massless excitations in all channels, and strict Gauss‑law invariance of all observables (violations below 10⁻¹⁰). The vacuum energy density remains finite and stable, confirming the absence of critical behavior. All these results satisfy the seven audit gates introduced in Part XXIV and extended to observables in Part XXV.</p> <p dir="ltr">Wilson loops are incorporated in Part XXVI not as primary diagnostics, but as secondary IR‑sensitive observables. Using the σ‑generator protocol introduced in Part XXV, we extract the dimensionless lattice area‑law coefficient σ̂ = 0.99 ± 0.34, reported strictly in lattice units. No physical normalization of σ is performed, because scale‑setting is intentionally deferred to Part XXVII. This corrects the inconsistency that appeared in earlier drafts of Part XXVI, where σ was prematurely converted into physical units.</p> <p dir="ltr">The central conceptual result of this work is the formalization of the spectral–geometric hierarchy:<br>spectral confinement is primary, determined by the mass gap, exponential clustering, finite correlation length, and absence of massless modes;<br>geometric confinement is emergent, with area‑law behavior appearing only in the infinite‑volume limit;<br>and Wilson loops cannot override spectral diagnostics, serving instead as IR refinements.</p> <p dir="ltr">To operationalize this hierarchy, we introduce Algorithm 1, a traffic‑light confinement protocol that integrates the seven‑gate audit of Part XXV with the spectral–geometric logic of Part XXVI. The algorithm provides a reproducible, audit‑ready procedure for diagnosing confinement in Hamiltonian gauge theories.</p> <p> </p> <p><a href="https://zenodo.org/records/18519299"><span dir="auto"><span dir="auto"><strong></strong></span></span></a></p> <p> </p> <ul> <li> <p dir="ltr"><strong>Keywords</strong>: Spectral Vacuum Mechanism; SU(3) Hamiltonian; continuum limit; non‑perturbative gap; Gaussian sector; solver robustness; volumetric stability; failure map; lattice truncation; spectral methods.</p> <p dir="ltr"> </p> <p dir="ltr"><strong>Other works by the author on this topic</strong></p> <p dir="ltr">Spectral Vacuum Mechanism (SVM) — Author’s Series</p> <ul> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XIV: Spectral Confinement as a Necessary Condition for Quantum Field Theory. Confinement Gate‑Induced Spectral Localization and Dimensional Constraints, Zenodo. DOI: 10.5281/zenodo.18140235 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XV: Unification of the Mass Formula in SVM Particles of the Standard Model, Zenodo. DOI: 10.5281/zenodo.18207487 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XVI: Spectral Confinement under Truncated SU(2) Gauge Embedding: Preservation of the Spectral Confinement Class, Zenodo. DOI: 10.5281/zenodo.18225421 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XVII: Spectral Confinement under Truncated SU(3) Gauge Embedding: Toward a Constructive QCD‑like Framework, Zenodo. DOI: 10.5281/zenodo.18280887 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XVIII: Continuum Trajectory and Low‑Energy Self‑Consistency under SU(3) Truncation, Zenodo. DOI: 10.5281/zenodo.18415826 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XIX: Gauss‑Law Certificates and Audit Artifacts under SU(3) Truncation, Zenodo. DOI: 10.5281/zenodo.18422292 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XX: SU(3) Truncation Removal: Controlled j_max → ∞ at Fixed (a, V) in the Physical Sector, Zenodo. DOI: 10.5281/zenodo.18434530 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XXI: Thermodynamic Limit (V → ∞) at Fixed Lattice Spacing in the Gauss‑Law Sector, Zenodo. DOI: 10.5281/zenodo.18444149 (2026).</p> </li> <li> <p dir="ltr">Spectral Vacuum Mechanism — Part XXII: Ultraviolet Stability and the Continuum Limit, Zenodo. DOI: 10.5281/zenodo.18448953 (2026).</p> </li> <li>Spectral Vacuum Mechanism — Part XXIII: At Finite Density: Hamiltonian Deformation and Phase Transitions, Zenodo. DOI: 10.5281/zenodo.18450115 (2026).</li> <li> </li> <li>Spectral Vacuum Mechanism — Part XXIV: Validation of the Continuum Trajectory: Kinetic Scaling, Gauss-Law Purity, Solver Robustness, and Failure Map, <span>Published February 2, 2026 </span><span>| Version v1, Zenodo. DOI: 10.5281/zenodo.18459836 (2026).</span></li> <li> </li> <li>Spectral Vacuum Mechanism — Part XXV: Spectral Observables in the Continuum SU(3) Hamiltonian: Correlators, Gauss-filter Operators, Susceptibilities, and Observable-Level Audit, <span>Published February 5, 2026 </span><span>| Version v1, Zenodo. DOI: 10.5281/zenodo.18498737 (2026).</span></li> </ul> <p dir="ltr"> </p> </li> </ul>