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

We present a major computational advance in solving the Boolean Pythagorean Triples Problem using the novel Amanollahi Methodology. This continuous optimization framework verifies the critical case n = 7825 using only 2 GB of memory — achieving a 100,000× memory reduction and 240× speedup over prior SAT-based methods. Crucially, we disprove the previously accepted threshold n = 7824, showing that a valid 2-coloring avoiding monochromatic Pythagorean triples does not exist. Our approach removes the need for supercomputers and enables future work on Ramsey-type problems using standard consumer hardware.