1 Introduction

GIFT (Geometric Information Field Theory) is a framework that derives Standard Model parameters from \(E_8\times E_8\) gauge theory compactified on \(G_2\)-holonomy manifolds. This blueprint documents the formal verification in Lean 4, providing:

• Mathematical definitions linked to Lean declarations

• Theorem statements with proof status (proven/axiom)

• Dependency graph for tracking proof progress

The key insight is that the topological invariants of \(G_2\)-manifolds (Betti numbers \(b_2= 21\), \(b_3= 77\)) combined with exceptional Lie group dimensions determine physical parameters with remarkable precision.