Abstract The dimensionality of spacetime is usually postulated rather than derived. In this work we show that within the spectral reconstruction protocol the ultraviolet spacetime dimension is selected dynamically as a compatibility optimum of the spectral data. The analysis is based on the ultraviolet heat-trace expansion and the Seeley–DeWitt reconstruction basis span{1, t, t²}. We introduce a compatibility functional Ψ(d) = sup_{W_uv} ε_rel(d, W_uv) which measures the maximal reconstruction residual across admissible ultraviolet windows. We demonstrate that this functional possesses a unique minimum at dimension d = 4. The effective spectral dimension defined from the heat trace, d_eff(E) = −2 d ln P(E^{−1}) / d ln E generates an associated spectral beta-function β_spec(d_eff) = d d_eff / d ln E We prove that the compatibility minimum coincides with the ultraviolet fixed point of this flow. Furthermore, we establish a spectral monotonicity principle showing that the compatibility functional acts as a Lyapunov quantity, ensuring irreversible approach to the ultraviolet dimension. The result establishes a variational–RG characterization of the ultraviolet dimension: within the admissible spectral reconstruction class the ultraviolet spacetime dimension is uniquely selected as the point where spectral incompatibility is minimized, the spectral beta-function vanishes, and the compatibility flow reaches its stable endpoint. Keywords: spectral geometry, spectral dimension, heat-trace expansion, Seeley–DeWitt coefficients, spectral reconstruction, compatibility functional, ultraviolet fixed point, renormalization group, variational principle, quantum gravity. Other works by the author on this topic:: [1] M. Nemirovsky, Spectral Vacuum Mechanism – Part XXVII: Metric from Spectral Overlaps, Zenodo. DOI: 10.5281/zenodo.18560958 (2026) [2] M. Nemirovsky, Spectral Vacuum Mechanism – Part XXVIII: Emergent Gauge Structure, Zenodo. DOI: 10.5281/zenodo.18599116 (2026) [3] M. Nemirovsky, Spectral Vacuum Mechanism – Part XXX: Emergent Gravity, Zenodo. DOI: 10.5281/zenodo.18636847 (2026) [4] M. Nemirovsky, Spectral Vacuum Mechanism – Part XXXVII: Phase Geometry and Quantization, Zenodo. DOI: 10.5281/zenodo.18769976 (2026) [5] M. Nemirovsky, Spectral Vacuum Mechanism – Part XXXIX: UV–4D Emergence as a Stable Spectral Property of the SVM Vacuum Hessian, DOI: 10.5281/zenodo.18861827 (2026) [6] M. Nemirovsky, Spectral Vacuum Mechanism – PART XL Spectral Compatibility and Dimensional Necessity: Internal Consistency of the UV–4D Framework, DOI: 10.5281/zenodo.18889765 (2026)