A PNAS paper introduces cuLoRADS, a GPU-accelerated low-rank alternating-direction splitting solver designed to break semidefinite programming's scale bottleneck through algorithm-hardware co-design. Some MaxCut instances run in 10 seconds to one minute on an 80 GB NVIDIA H100 where reported CPU solvers took tens of hours; the system also handles huge matrix-completion and MaxCut instances in minutes and clears an 18-year computational barrier in quantum ordered search. The authors report up to four orders of speed and scalability gain for specific sparse, low-rank structures, not every optimization task.