Pseudo-deterministic PRG-XOR Isolation: A Rigorous Framework for Unique-SAT

A pseudo-deterministic framework for isolating satisfying assignments of Boolean formulas using sparse XOR constraints generated by a pseudo-random generator (PRG). Combines k-sparse PRG-XOR matrices with a deterministic Pseudo-deterministic Stability Test (PST) to ensure high-probability full-rank matrices and negligible constraint removal, providing reproducible XOR-based isolation without unconditional derandomization.