Hyperspectral image super-resolution (HSI-SR) aims to recover spatial detail while preserving the spectral shape on which quantitative analysis relies. Recent HSI-SR methods, from repurposed RGB super-resolution backbones to dedicated spectral-spatial architectures, have greatly improved spatial reconstruction. However, overlooking the compact spectral structure of hyperspectral data leaves residual spectral errors, while binding the spectral treatment to each architecture forces it to be rebuilt for every new backbone. Yet the low-dimensional structure of spectra belongs to the data, not to any backbone. Backbones differ in the errors they leave, but not in the structure of the true spectra. One rectifier design can therefore serve any backbone. Building on this insight, we propose the \textbf{S}pectral \textbf{R}ectification \textbf{S}uper-\textbf{R}esolution Network (\textbf{SR$^{2}$-Net}), a model-agnostic rectifier that needs nothing from the backbone but its output, leaves its internal architecture untouched, and is trained per backbone. SR$^{2}$-Net follows an \emph{enhance-then-rectify} pipeline in which Hierarchical Spectral-Spatial Synergy Attention (\textbf{H-S$^{3}$A}) reinforces cross-band interactions, while Mode-Constrained Rectification (\textbf{MCR}) confines the correction to a learned compact spectral subspace. A degradation-consistency constraint further ties the output to the observed low-resolution input. Experiments with five backbones spanning CNN, Transformer, and diffusion families show that one fixed configuration improves spectral fidelity in every reported setting while preserving or improving spatial quality. Averaged over thirty in-domain settings, SR$^{2}$-Net removes 22.6\% of the residual spectral error at a backbone-independent cost of 0.048M parameters.

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