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This file presents a preprint of a proposed proof that P = NP by providing a polynomial-time algorithm for the Positive 1-in-3 SAT problem. I aimed to convey that, in the absence of duplicate variables and clauses, the maximum number of clauses depends on nnn, which creates the possibility of a "threshold" beyond which the formula becomes UNSAT. Three main cases are identified, covering the entire family of Positive 1-in-3 SAT instances, two of which can be solved in constant time, and the third in polynomial time. I am not certain to what extent I have been able to translate my thoughts into formal language, but I hope that the direction of my idea will be clear.