What if physics isn't fine-tuned, just well-shaped?
GIFT explores whether the dimensionless parameters of the Standard Model may be topological invariants of a single compact 7-manifold: an E₈×E₈ gauge theory on a G₂-holonomy manifold K₇ with Betti numbers (b₂, b₃) = (21, 77). No fitting, no free parameters — each prediction is a consequence of shape, and each is individually correct-or-wrong.
The compact exceptional holonomy chain G₂ ⊃ SU(3) ⊃ SU(2) ⊃ U(1) and the Betti data of K₇ that fix the integers entering the parameter-free core.
- Zero free parameters — Standard Model dimensionless parameters expressed as topological invariants of K₇, (b₂, b₃) = (21, 77).
- Machine-checked — 15 Lean-4 axioms (4 on the prediction chain + 11
interval-arithmetic certificates for the K3 block), 0
sorry, 460+ certified relations. - 33 exact relations among topological integers — the parameter-free core; each individually falsifiable, none tunable.
- Falsifiable — δ_CP = 197°, N_gen = 3, θ₂₃ upper octant; decided by DUNE / FCC-ee.
- Non-generic — among 3,000,000 random algebraic formula sets drawn from the framework's own vocabulary, none reproduces its joint profile (set-level upper bound ≈ 10⁻⁶, no independence assumption).
- Precision (secondary): 0.92% mean deviation on the 33 Type-I relations; 95 observables total, 66 with experimental data. (NuFIT 6.1 / PDG 2024 / Planck 2018 / CODATA 2022 · core v3.4.26)
Cited in the peer-reviewed literature. Heyes, Hirst, Sá Earp & Silva, Phys. Lett. B 878 (2026) 140566 (Imperial College London / UNICAMP)
Invited remote participant, "DANGER: Data, Numbers, and Geometry" workshop Banff International Research Station (BIRS), April 5–10, 2026.
| ✅ Proven (Lean 4) | 🔢 Computed (numeric) | 🔭 Conjectured | ⚖️ Falsifies |
|---|---|---|---|
| 33 exact relations among topological integers | Closed-form K3 metric witness, order-3 ansatz | E₈×E₈ → K₇ compactification realizes the SM | δ_CP = 197° → DUNE (2028–2040) |
| K3 interval certificates (Krawczyk containment, variance envelope ≤ 1321/10⁷) | 95-observable table, 0.92% mean deviation (Type I) | Full smooth compact G₂ analytic construction of (21, 77) — open | θ₂₃ in the upper octant → DUNE / NuFIT |
G₂ lattice & isotype certificates · 0 sorry |
Volume-form residual certified interval-rigorous on a frozen box-local witness | Physical reading of the topological coupling κ_T | N_gen = 3 |
| 🌍 Curious? | → GIFT — the framework, plain-language guides, documentation, statistical validation |
| 📐 Want the proofs? | → core — the Lean 4 formalization and giftpy |
pip install giftpyfrom gift_core import *
print(SIN2_THETA_W) # Fraction(3, 13)
print(GAMMA_GIFT) # Fraction(511, 884)
print(TAU) # Fraction(3472, 891)| giftheory.substack.com | Essays on topology, physics, and the research process |
| @giftheory | Video introductions to the framework |
| @GIFTheory | Automated facts from the framework, twice a week |
- GIFT v3.4 — Standard Model Parameters as Topological Invariants of a G₂ Holonomy Manifold DOI: 10.5281/zenodo.20070101
- Paper A — A Certified Torsion-Free G₂ Structure on a TCS Neck Model DOI: 10.5281/zenodo.19892350
- Paper B — Spectral Geometry of an Explicit G₂ Metric: Laplacian Spectrum and Harmonic Forms DOI: 10.5281/zenodo.19893371
- Paper C — Newton–Kantorovich Diagnostics on a Donaldson K3 Metric DOI: 10.5281/zenodo.19708916
- Paper D — Donaldson Analytic Note: explicit closed-form G₂ ansatz with Wirtinger certificate DOI: 10.5281/zenodo.20039066
- Heyes, Hirst, Sá Earp & Silva — Neural and numerical methods for G₂-structures on contact Calabi–Yau 7-manifolds, Phys. Lett. B 878 (2026) 140566 (Imperial College London / UNICAMP)
- Zhou & Zhou — Algebraic Stability and Cosmological Structure (2026): derive (b₂, b₃) = (21, 77) from self-referential dynamics, citing GIFT as empirical motivation
- Mamun — The Void Paradox: Towards a Universal Coordinate System for Information Reality (2026), University of Oxford
- Cabannas & Silva — The Modal Discipline of Objectivity (2026), UFBA / UFMA
- Blueprint — Lean formalization dependency graph
- giftpy on PyPI —
pip install giftpy - Zenodo — canonical publications (framework v3.4)
If this resonates, star the repos so others find it. Try it in ten seconds with
pip install giftpy, and follow the story on Substack.
GIFT FROM BIT