An Unconditional Proof Rooted in the Laws of Complexity and Compression
For decades, the P vs NP problem has haunted mathematics and computer science: Can every problem whose solution can be verified quickly also be solved quickly? Most experts believe the answer is no—P is not equal to NP—but no proof has withstood scrutiny. Until now.
A new proof tackles the question not through exotic logic or brute-force argumentation, but by using a deep principle from information theory: entropy. It constructs specific problems whose solution spaces are so disordered—so saturated with randomness—that no algorithm can compress them or navigate them efficiently. This entropy imposes an unavoidable cost on discovery: exponential time. The framework rigorously connects entropy to decision trees, circuit size, and communication complexity. It even anticipates and neutralizes advanced threats like quantum algorithms and machine learning. The result? A fully unconditional proof that P ≠ NP, grounded not in guesswork, but in the fundamental limits of information itself.