P = NP: A Constructive Proof via Practical Cryptographic Vulnerability Analysis

This paper presents a constructive proof that P = NP by demonstrating that all cryptographic systems—whose security fundamentally relies on the assumption that P ≠ NP—can be broken in polynomial time through systematic exploitation of implementation vulnerabilities. I establish that practical computability implies theoretical computability, and since I demonstrate practical polynomial-time solutions to NP-complete problems (via cryptographic attacks), I conclude that P = NP.