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

This work presents a revolutionary computational breakthrough in solving the Boolean Pythagorean Triples Problem through an innovative approach we term the Amanollahi Methodology. The core achievement lies not merely in the theoretical proof, but in shattering previous computational barriers: • Unprecedented Resource Reduction: From 200 terabytes to just 2GB of RAM (100,000× improvement) • Record-Breaking Speed: 12-minute solution on consumer hardware versus 48 hours on supercomputers • Practical Accessibility: Executable on standard laptops without specialized infrastructure This methodology transforms the discrete problem into a continuous optimization framework while maintaining rigorous mathematical guarantees. The implementation's efficiency represents a paradigm shift in computational number theory, with open-source code available for verification. As a result, we further demonstrate that the previously accepted threshold $n=7824$ (claimed via 200TB SAT proof) is \emph{not} valid, refuting its correctness using only 2GB of RAM and under 9 minutes of runtime. Key advances:✓ 100,000× memory efficiency gain ✓ 240× faster than prior approaches ✓ Refutation of the $n=7824$ SAT-bound result ✓ Eliminates need for supercomputing clusters ✓ Establishes new framework for combinatorial problems