We quantify the transition between weak and strong coupling in thermal $\mathcal{N}=4$ supersymmetric Yang-Mills theory in four space-time dimensions by constructing an admissible ensemble of log-aware Padé approximants that incorporate the weak- and strong-coupling expansions through $\mathcal{O}({\lambda }^2)$ and $\mathcal{O}({\lambda }^{-3/2})$ ($\lambda$ is the ’t Hooft coupling), including the nonanalytic ${\lambda }^{3/2}$ and ${\lambda }^2\log \lambda$ terms. This replaces single-curve estimates with a reproducible uncertainty band and a well-defined central curve across the intermediate regime. The framework is predictive, setting testable benchmarks for forthcoming perturbative and holographic calculations.

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• Feynman diagrams
• Finite temperature field theory
• Resummation methods
• Supersymmetric field theories