A Deterministic Oracle Machine Resolving NP via Binary Search on an Ordered Solution Space

We present a construction of a deterministic Turing machine augmented with an oracle that resolves any instance of 3-SAT — and by Karp reduction, any NP-complete problem — in O (n) time, where n is the number of variables. The oracle is defined as a precise binary search function over a lexicographically ordered enumeration K of all possible assignments. We formalize the exact oracle function, prove its existence, and derive the implication P = NP.