GIFT: Geometric Information Field Theory

Part of the Arithmon program - the hypothesis that the constants of nature are counts.

GIFT explores whether Standard Model dimensionless parameters may be topological invariants of an E₈ × E₈ gauge theory compactified on a G₂-holonomy manifold K₇, with zero free parameters. The parameter-free core is 33 exact relations among topological integers, machine-checked in Lean 4: 460+ certified relations, 15 axioms (4 on the prediction chain + 11 interval-arithmetic K3 certificates), 0 sorry. Precision (secondary): 0.99% mean deviation on the 33 Type-I relations (NuFIT 6.1 / PDG 2024 / Planck 2018).

Quick Links

GIFT Blueprint - Dependency graph visualization
Blueprint (web) - Lean blueprint with proofs
Blueprint (pdf) - Downloadable PDF
Dependency Graph - Proof dependencies
API Documentation - Lean code documentation

Key Results

Constant	GIFT Value	Measured	Deviation
sin²θ_W	3/13 ≈ 0.2308	0.2312	0.17%
α_EM⁻¹	137.036…	137.036	<0.001%
n_s	ζ(11)/ζ(5) ≈ 0.965	0.965	0.03%

Repository Structure

gift-framework/core/
├── GIFT/           # Lean 4 formal proofs (144 files, 460+ relations, 15 axioms)
├── GIFTTest/       # Lean test files
├── contrib/        # Python package, blueprint, homepage
└── lakefile.lean   # Lake build configuration

Getting Started

# Clone the repository
git clone https://github.com/gift-framework/core.git
cd core

# Build Lean proofs
lake build

# Install Python package
pip install giftpy