We introduce CORTEX, an algorithmic framework designed for large-scale brain simulation. Leveraging the computational capacity of the Fugaku Supercomputer, CORTEX maximizes available problem size and processing performance. Our primary innovation, Indegree Sub-Graph Decomposition, along with a suite of parallel algorithms, facilitates efficient domain decomposition by segmenting the global graph structure into smaller, identically structured sub-graphs. This segmentation allows for parallel processing of synaptic interactions without inter-process dependencies, effectively eliminating data racing at the thread level without necessitating mutexes or atomic operations. Additionally, this strategy enhances the overlap of communication and computation. Benchmark tests conducted on spiking neural networks, characterized by biological parameters, have demonstrated significant enhancements in both problem size and simulation performance, surpassing the capabilities of the current leading open-source solution, the NEST Simulator. Our work offers a powerful new tool for the field of neuromorphic computing and understanding brain function.