Formal Proof Sketch for P ≠ NP Using Information Flow and Physical Constraints

This document presents a novel approach to the P ≠ NP problem through a dual framework combining physical and information-theoretic lower bounds. The proof sketch relies on an entropy-based argument and information flow limitations on Turing machines. It also incorporates communication complexity and circuit lower bound techniques, including an extended application of the Karchmer–Wigderson game. The work is intended as a contribution to the theoretical understanding of computational intractability and proposes a foundation for formalization in proof assistants like Lean or Coq.