giftpy on PyPI Lean 4 verified License: MIT
Part of the Arithmon program — the hypothesis that the constants of nature are counts.
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 ×ばつ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 dimensional-reduction chain G2 ⊃ SU(3) ⊃ SU(2) ⊃ U(1) and the topological data of K7
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): 0.99% 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 | ×ばつE8 → K7 compactification realizes the SM | δ_CP = 197° → DUNE (2028–2040) |
| K3 interval certificates (Krawczyk containment, variance envelope ≤ 1321/107) | 95-observable table, 0.99% 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 giftpy
from gift_core import * print(SIN2_THETA_W) # Fraction(3, 13) print(GAMMA_GIFT) # Fraction(511, 884) print(TAU) # Fraction(3472, 891)
| arithmon.substack.com | Essays on topology, physics, and the research process |
| @arithmon | 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)
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GIFT is the founding framework of the Arithmon program.
GIFT FROM BIT