The Mathematics of Function Growth Branches: A Geometric Proof of P ≠ NP

We establish a formal framework called "The Mathematics of Function Growth Branches" based on ten axioms of cognitive topology. We construct a boundary obstruction class on a four-dimensional cognitive manifold and prove that its non-vanishing implies P ≠ NP. The proof relies solely on topological curvature integrals and the observer endofunctor iteration, with no computational assumptions. Full details, including all theorems and verification code, are included in the PDF.