λk-Driven Incompressibility: Lower Bounds Separating P from NP

We propose a novel complexity framework based on information-theoretic structure compres- sion to analyze the distinction between P and NP problems. Central to our model is a structural compressibility indicator λk(x), derived from Kolmogorov complexity approximations of problem instances and their solutions. We introduce the structure-time coupling Λ(x), and conjecture a time lower bound T(x) ≥Ω(n2 ·2λk (x)). Empirical regression analysis confirms this relation with near-perfect fit, suggesting a structural foundation for proving that P ̸= NP.