Deterministic Framework toward P = NP: A Polynomial-Time Uniqueness Test and Explicit Linear Isolation Scheme

This technical report presents a deterministic framework addressing the P vs NP question strictly within the classical Turing model.The work introduces a polynomial-time uniqueness test based on linear algebra over GF(2), an explicit linear hashing family ensuring isolation of single satisfying assignments, and a deterministic SAT→Unique-SAT reduction that removes randomization from the Valiant–Vazirani isolation method. The proposed framework provides a fully verifiable and computationally bounded pathway toward derandomization in complexity theory.It unifies ideas from small-bias combinatorics, perfect hashing, and algebraic constraint propagation.The report concludes with a worked example and outlines two open lemmas—the deterministic isolation guarantee and formal correctness of the uniqueness test—that, once proven, would yield a complete deterministic route to SAT ∈ P and therefore P = NP.