Digital Rock Physics (DRP) requires high-fidelity pore-scale imaging, yet micro-computed tomography ($\mu$-CT) trades spatial resolution against field of view, and standard super-resolution (SR) often fails to preserve transport-controlling pore topology. We propose Vision-LSTM and State-Space Super-Resolution (ViSSR), a physics-informed hybrid residual SR network that couples Vision-LSTM (ViL) for local anisotropic texture with a Mamba-based 2D selective state-space module (SS2D) for linear-complexity global context, and restores high-frequency structure via scale-conditioned residuals under an explicit partial-volume and PSF degradation model. Because reconstruction errors propagate into permeability and flow analysis, we report the pixel metrics PSNR, SSIM, and LPIPS together with topology-aware scores comprising pore-size-distribution earth mover’s distance (PSD-EMD; one-dimensional Wasserstein-1), porosity, connectivity, spanning, and fractal dimension. On DeepRock-SR, ViSSR attains 32.08 dB PSNR, 0.746 SSIM, and 0.04 PSD-EMD at $\times 4$, and preserves pore topology across sandstone, carbonate, and coal where perceptual baselines hallucinate or oversmooth. Zero-shot slice-stacked reconstruction on independently acquired dual-resolution carbonates from MRCCM, project DRP-362, further yields volumetric transport gains over bicubic upsampling under scanner-realized $\times 4$ degradation.