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gift-framework/GIFT

Geometric Information Field Theory

License Lean 4

What if physics isn't fine-tuned, just well-shaped?

GIFT derives Standard Model parameters from the geometry of a single 7-dimensional manifold. No free parameters. No fitting. Every prediction is a consequence of shape: E₈×E₈ gauge theory compactified on a G₂-holonomy manifold K₇ with Betti numbers (b₂, b₃) = (21, 77).


Start Here

Watch (8 min) Read the blog
GIFT for Everyone FAQ

Blog

All posts on giftheory.substack.com.

Post Topic
"The author's name appears to be fabricated" Learning Physics with AI: the accidental origin of GIFT
The Geometry of the Impossible What Roberto Carlos Knew (Without Knowing It)
The Lice of the Universe What We Cannot Perceive, and What That Means
The Algebra That Waited On octonions, patience, and a 43-year puzzle
Gift from Bit Why geometry might be the language of physics
13 Theorems, Zero Trust Required Machine-verified proofs in Lean 4
Joyce's Theorem, Now in Lean Formalizing G₂ holonomy existence
On What Comes First Philosophy of mathematical primacy

For Specific Audiences

Background Start Here
Everyone GIFT for Everyone -- Complete guide with everyday analogies
Physicist Info Geo for Physicists -- Topological approach to SM parameters
Geometer GiftPy for Geometers -- G₂ metric construction pipeline
Formalization Lean for Physics -- Machine-verified physical relations

Papers

Document Description
Main Paper (PDF) Complete theoretical framework
S1: Foundations (PDF) E₈, G₂, K₇ mathematical construction
S2: Derivations (PDF) All 33 derivations (0.24% mean, PDG 2024 / NuFIT 6.0)
Explicit G₂ Metric (PDF) Analytical G₂ metric construction
Spectral Geometry (PDF) KK spectrum, Yukawa, gauge unification from G₂ metric

At a Glance

Precision 0.24% mean deviation across 32 well-measured observables (PDG 2024 / NuFIT 6.0)
Observables 92 total (66 with experimental comparison)
Parameters Zero adjustable (all structurally determined)
Verified 130 Lean 4 files, 7 axioms, zero incomplete proofs (core v3.4.5)
Uniqueness #1 out of 3,070,396 configurations tested

Dimensional reduction: E₈×E₈ (496D) → AdS₄ × K₇ (11D) → Standard Model (4D)


Key Results

Exact Relations (Lean 4 Verified)

Relation Value Topological Origin
sin²θ_W 3/13 b₂/(b₃ + dim(G₂))
κ_T 1/61 1/(b₃ − dim(G₂) − p₂)
τ 3472/891 (496 × 21)/(27 × 99)
det(g) 65/32 Metric determinant from G₂ structure
δ_CP 197° 7 × dim(G₂) + H*
m_s/m_d 20 p₂² × w
Q_Koide 2/3 dim(G₂)/b₂

Precision by Sector

Sector Predictions Mean Deviation Highlight
Electroweak 3 0.12% sin²θ_W = 3/13
Lepton 3 0.04% Q_Koide = 2/3 (0.0009%)
Quark 1 0.00% m_s/m_d = 20 (exact)
Neutrino 3+1 0.25% + δ_CP at 1σ θ₁₂ = arctan(2/3)
Cosmology 3 0.07% n_s = ζ(11)/ζ(5) (0.004%)
Structural 4 exact N_gen = 3, τ = 3472/891

Analytical G₂ Metric

Property Value Status
Associative 3-form φ = (65/32)^{1/14} × φ₀ EXACT
Metric g = (65/32)^{1/7} × I₇ EXACT
Torsion T = 0 (constant form) EXACT
det(g) 65/32 EXACT

Statistical Uniqueness

Exhaustive Search

Metric Value
Configurations tested 3,070,396
GIFT rank #1
Mean deviation 0.24% (32 well-measured)
Better alternatives found 0

Top 5 Configurations

Rank b₂ b₃ Deviation
1 21 77 0.24%
2 21 76 0.50%
3 21 78 0.50%
4 21 79 0.79%
5 21 75 0.81%

Statistical Significance

Test Result
Null model p-value < 2×10⁻⁵ (σ > 4.2), three independent null families
Westfall-Young maxT 11/33 individually significant (global p = 0.008)
Pre-registered test split p = 6.7×10⁻⁵ (σ = 4.0)
Bayes factor 304–4,738 across four priors (all decisive)
Exhaustive search 0/3,070,396 configs better

Details: Statistical Evidence


Falsification Tests

Prediction Experiment Timeline Falsification Criterion
δ_CP = 197° DUNE 2027-2030 Outside [187°, 207°]
sin²θ_W = 3/13 FCC-ee 2040s Outside [0.2295, 0.2320]
m_s/m_d = 20 Lattice QCD 2030 Converges outside [19, 21]
N_gen = 3 LHC Ongoing Fourth generation discovery

Limitations

The framework contains no continuous adjustable parameters fitted to data. However, it makes discrete structural choices: E₈×E₈ as gauge group, K₇ with (b₂=21, b₃=77), TCS building blocks. These are mathematically motivated but constitute model selection. The framework predicts observables given these choices: it does not explain why nature chose this geometry.

Statistical validation shows (b₂=21, b₃=77) is the unique optimum among 3,070,396 tested configurations. This doesn't explain the choice, but establishes it is not arbitrary.


Related Repositories

Repository Description
gift-framework/core Formal verification (Lean 4), K₇ metric pipeline, giftpy

Connect

Platform
Substack giftheory.substack.com
YouTube @giftheory
X @GIFTheory
Archive
Zenodo (framework) 10.5281/zenodo.18837071
Zenodo (explicit G₂ metric) 10.5281/zenodo.18860358
Zenodo (spectral geometry) 10.5281/zenodo.18920368
ResearchGate Author page

Citation

@software{gift_framework,
  title   = {GIFT: Geometric Information Field Theory},
  author  = {de La Fournière, Brieuc},
  year    = {2026},
  url     = {https://github.com/gift-framework/GIFT},
  version = {3.4}
}

See CITATION.md for additional formats.


License

MIT License, see LICENSE


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