giftpy 3.1.8

GIFT mathematical core - Formally verified constants (Lean 4 + Coq)

GIFT Core

Formally verified mathematical relations from the GIFT (Geometric Information Field Theory) framework. All relations are proven in both Lean 4 and Coq.

Overview

This repository contains 180+ exact mathematical identities derived from topological invariants of E₈ gauge theory on G₂ holonomy manifolds.

Core Results

• 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)

Extensions

• 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

Infrastructure

• Dual Verification: All theorems proven in Lean 4 + Coq
• Blueprint: Dependency graph with 185 linked declarations (leanblueprint)
• Python Package: giftpy with certified constants

Installation

pip install giftpy

Quick Start

from gift_core import *

# Certified constants
print(SIN2_THETA_W)   # Fraction(3, 13)
print(KAPPA_T)        # Fraction(1, 61)
print(GAMMA_GIFT)     # Fraction(511, 884)

Building Proofs

# Lean 4
cd Lean && lake build

# Coq
cd COQ && make

Documentation

• Changelog
• Usage Guide
• Full Framework

Acknowledgments

Blueprint structure inspired by KakeyaFiniteFields.

License

MIT

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GIFT Core v3.1.8