The paper presents a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, similar to the continuous variable cat encoding. This approach aims to correct dominant error sources, such as linear and quadratic operators in angular momentum, which are common in spin systems. The key components include a rank-preserving CNOT gate and a measurement-free error correction scheme for amplitude errors. The authors demonstrate that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. They propose a specific implementation using neutral-atom quantum computing, encoding the qubit in the nuclear spin of 87Sr, and show how to generate the universal gate set, including the rank-preserving CNOT gate, using quantum control and Rydberg blockade. The findings suggest that encoding a qubit in a large spin can achieve fault tolerance, high thresholds, and reduced resource overhead in quantum information processing.The paper presents a fault-tolerant quantum error-correcting protocol based on a qubit encoded in a large spin qudit using a spin-cat code, similar to the continuous variable cat encoding. This approach aims to correct dominant error sources, such as linear and quadratic operators in angular momentum, which are common in spin systems. The key components include a rank-preserving CNOT gate and a measurement-free error correction scheme for amplitude errors. The authors demonstrate that the fault-tolerant threshold for error correction in the spin-cat encoding surpasses that of standard qubit-based encodings. They propose a specific implementation using neutral-atom quantum computing, encoding the qubit in the nuclear spin of 87Sr, and show how to generate the universal gate set, including the rank-preserving CNOT gate, using quantum control and Rydberg blockade. The findings suggest that encoding a qubit in a large spin can achieve fault tolerance, high thresholds, and reduced resource overhead in quantum information processing.