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.

This is a corrected version (v2) with a complete axiom system (Chapter 0) and a geometric construction of 3-SAT (Chapter 1).

Version v2 – 2026.07.27

This is a further revision (v3) based on v2. 
It adds Appendix J, which provides formal definitions of:
- the cognitive fiber bundle E (derived from Axiom 7)
- the boundary obstruction class 𝔒_{P/NP} (derived from Axiom 5)

No new axioms are introduced. This revision completes the formalization of all symbols used in the main proof.