Formally verified mathematical relations from the GIFT (Geometric Information Field Theory) framework. All relations are proven in both Lean 4 and Coq.
This repository contains 180+ exact mathematical identities derived from topological invariants of E₈ gauge theory on G₂ holonomy manifolds.
- Explicit G₂ Metric: Closed-form solution g = (65/32)^{1/7} × I₇ with det(g) = 65/32 and zero torsion
- E₈ Root System: Complete enumeration (240 = 112 + 128) with Weyl reflection theorems
- G₂ Cross Product: 7D Lagrange identity ‖u × v‖² = ‖u‖²‖v‖² - ⟨u,v⟩² proven via coassociative 4-form
- Joyce Existence: K₇ admits torsion-free G₂ structure (Banach fixed-point formalization)
- Sequence Embeddings: Fibonacci F₃–F₁₂ and Lucas L₀–L₉ map to GIFT constants
- Prime Atlas: 100% coverage of primes < 200 via three generators (b₃, H*, dim_E₈)
- Monstrous Moonshine: 196883 = 47 × 59 × 71, j-invariant 744 = 3 × dim_E₈
- McKay Correspondence: E₈ ↔ Binary Icosahedral ↔ Golden Ratio
- Dual Verification: All theorems proven in Lean 4 + Coq
- Blueprint: Dependency graph with 185 linked declarations (leanblueprint)
- Python Package:
giftpywith certified constants
pip install giftpyfrom gift_core import *
# Certified constants
print(SIN2_THETA_W) # Fraction(3, 13)
print(KAPPA_T) # Fraction(1, 61)
print(GAMMA_GIFT) # Fraction(511, 884)# Lean 4
cd Lean && lake build
# Coq
cd COQ && makeBlueprint structure inspired by KakeyaFiniteFields.
MIT
GIFT Core v3.1.8
