A Polynomial-Time Ternary Logic Algorithm for Solving 3-SAT Problems: Towards a Constructive Resolution of the P versus NP Question

"Could solving NP-complete problems like 3-SAT be achievable within polynomial time using ternary logic?" We introduce a novel ternary logic algorithm ({-1, 0, +1}) combined with a degenerative heuristic designed to efficiently address the classical 3-SAT problem. Unlike traditional binary methods, our ternary approach incorporates an intermediate neutral state, effectively reducing the complexity of the search space and avoiding exponential runtime growth. Through rigorous theoretical analysis and extensive experimental validation on diverse scenarios (SAT, UNSAT, and intermediate cases), our results provide compelling evidence supporting polynomial-time complexity claims. While further large-scale validation remains necessary, this work offers a promising and constructive step forward in addressing the longstanding P vs NP question, with potential implications for fields such as cryptography, optimization, and artificial intelligence.