From 200TB to 2GB: Breaking Computational Barriers in the Boolean Pythagorean Triples Problem

We present a major computational breakthrough in solving the Boolean Pythagorean Triples Problem through the novel Amanollahi Methodology. This continuous optimization framework verifies the critical case n = 7825 using only 2 GB of memory — achieving a 100,000x reduction in memory usage and a 240x speedup compared to prior SAT-based methods. Furthermore, we provide a definitive refutation of the previously assumed satisfiable case n = 7824, establishing that no valid two-coloring exists. Our approach eliminates the dependence on supercomputing infrastructure and opens the door to tackling broader Ramsey-type problems on standard consumer hardware.