Deep-learning-based 3D MRI reconstruction is limited in practice by the GPU memory and compute cost of full-volume training; 3D acquisitions are thus most often reconstructed by 2D models applied slice-by-slice and then stacked, which ignores through-plane (stacking-axis) structure. We reconstruct in full 3D and ask whether a model can be trained at low resolution (fast and memory-feasible) yet deployed at higher resolution. This coarse-to-fine strategy needs reliable cross-resolution performance, but standard networks are resolution-specific and degrade substantially when evaluated outside the training setting. We therefore use resolution-agnostic neural operators (NOs) and propose KIR-NO (k-space-to-Image Reconstruction Neural Operator), a discretization-agnostic framework for accelerated 3D MRI reconstruction. KIR-NO is trained with full backpropagation on low-resolution volumes and applied zero-shot to higher-resolution volumes at inference. Its core building block is a 3D neural operator based on discrete-continuous convolutions: convolutional filters are parameterized in a continuous basis and sampled at arbitrary voxel resolutions while preserving the local inductive bias of convolution. KIR-NO integrates these learned operators with physics-based consistency: a k-space neural-operator head first refines the undersampled Fourier measurements, and image-space neural-operator cascades then refine the reconstruction through interleaved data-consistency updates. Across 3D knee and brain MRI benchmarks, KIR-NO improves over classical and CNN baselines: it improves over a state-of-the-art 3D CNN by 2.2 dB PSNR at half resolution under 4x acceleration on SKM-TEA, with gains persisting at 8x and 16x. These results show that resolution-agnostic operators make coarse-to-fine 3D MRI reconstruction - cheap low-resolution training with high-resolution deployment - practical across anatomies.

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