Amanollahi Methodology Implementation: Boolean Pythagorean Triples Verification (n=7825)

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.Our approach removes the need for supercomputers and enables future work on Ramsey-type problems using standard consumer hardware.