ABSTRACT Part XXV establishes the first complete gauge-invariant observable layer of the Spectral Vacuum Mechanism (SVM), enabling quantitative validation of the Hamiltonian framework developed in Parts XX–XXIV. The central achievement of this work is an independent correlator-based determination of the lightest scalar glueball mass, providing a non-spectral cross-check of the SVM continuum trajectory. For the 0⁺⁺ control channel, Euclidean correlator fits yield m_corr = 1.65 ± 0.05 GeV, in excellent agreement (≈1.8%) with the Hamiltonian mass M_phys = 1.68 ± 0.02 GeV obtained in Part XXII and validated along the continuum trajectory in Part XXIV. This constitutes the first internal consistency test between the spectral (Hamiltonian) and Euclidean correlator formulations of the SVM. A second major result is the demonstration of strict gauge invariance for all observables. Every operator constructed in Part XXV satisfies the commutator-based diagnostic |⟨0| [G_x^a, O] |0⟩| < 10⁻¹⁰, confirming that correlators, Wilson-loop operators, and susceptibilities remain entirely within the physical Gauss-law sector. Third, we introduce and validate Wilson-loop observables within the SVM (area-law diagnostic), providing a direct confinement observable. Using the σ-generator protocol (Appendix E), we extract the dimensionless area-law coefficient σ̂ = σ_latt = 0.99 ± 0.34, reported strictly as a dimensionless lattice quantity. Physical normalization of σ is intentionally deferred until an independent scale-setting procedure is introduced; in Part XXV, σ̂ serves as a qualitative confinement indicator. Fourth, we define spectral susceptibilities (χ_μ, χ_L, χ_crit) and evaluate them along the validated continuum trajectory. All susceptibilities remain smooth and bounded, indicating a stable, analytic, gapped vacuum with no evidence of critical behavior within the audited domain. All observables in Part XXV pass the full seven-gate audit standard (Gauss-law purity, truncation stability, solver robustness, finite-volume stability, channel stability, plateau stability, and continuum consistency). A complete systematic error budget is provided, and all statements are classified as Category A/B/C (rigorous / continuum-dependent / interpretational). Part XXV therefore establishes the first fully documented, gauge-invariant observable framework for the SVM, enabling the next stages of the series: multi-channel glueball spectroscopy (Part XXVI), spectral renormalization-group analysis (Part XXVII), and finite-temperature spectral dynamics (Part XXVIII). Keywords: Spectral Vacuum Mechanism (SVM); SU(3) Yang–Mills theory; Hamiltonian lattice gauge theory; gauge-invariant observables; Gauss-law sector projection; Euclidean correlators; glueball spectroscopy; Wilson loops and area law; string tension (dimensionless σ̂); reproducibility and observable-level audit. Other works by the author on this topic Spectral Vacuum Mechanism (SVM) — Author’s Series 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). Spectral Vacuum Mechanism — Part XV: Unification of the Mass Formula in SVM Particles of the Standard Model, Zenodo. DOI: 10.5281/zenodo.18207487 (2026). 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). 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). Spectral Vacuum Mechanism — Part XVIII: Continuum Trajectory and Low‑Energy Self‑Consistency under SU(3) Truncation, Zenodo. DOI: 10.5281/zenodo.18415826 (2026). Spectral Vacuum Mechanism — Part XIX: Gauss‑Law Certificates and Audit Artifacts under SU(3) Truncation, Zenodo. DOI: 10.5281/zenodo.18422292 (2026). 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). Spectral Vacuum Mechanism — Part XXI: Thermodynamic Limit (V → ∞) at Fixed Lattice Spacing in the Gauss‑Law Sector, Zenodo. DOI: 10.5281/zenodo.18444149 (2026). Spectral Vacuum Mechanism — Part XXII: Ultraviolet Stability and the Continuum Limit, Zenodo. DOI: 10.5281/zenodo.18448953 (2026). Spectral Vacuum Mechanism — Part XXIII: At Finite Density: Hamiltonian Deformation and Phase Transitions, Zenodo. DOI: 10.5281/zenodo.18450115 (2026). SPECTRAL VACUUM MECHANISM — PART XXIV Validation of the Continuum Trajectory: Kinetic Scaling, Gauss-Law Purity, Solver Robustness, and Failure Map, Zenodo. DOI: 10.5281/zenodo.18459836(2026).