The K₇ Framework
A zero-parameter framework deriving Standard Model constants from G₂ holonomy geometry.
At a Glance
| Property | Value |
|---|---|
| Predictions | 95 observables (33 Type I + 19 Type II + 21 Type III + 22 Type IV) |
| Mean deviation | 0.99% on 33 Type I (exact-target) relations (NuFIT 6.1 / PDG 2024 / Planck 2018 / CODATA 2022) |
| Free parameters | 0 (3 integer primitives: N=3, r₈=8, r₂=2) |
| Lean 4 verification | 146 files, 8394 build jobs, 0 sorry, 14 axioms at K7-Lean main (4 prediction-chain + 10 K3 interval certificates) (K7-Lean v3.5) |
| Statistical significance | p < 2×10⁻⁵ (σ > 4.2), unique among 3M+ configurations |
| Monte Carlo null model | P(algebraic) = 10⁻¹³⁸ over 3M+ formulas |
Quick Links
| New here? | Getting Started: Pick your path |
| Read papers | Paper Main Framework (Paper Explicit G2 Metric) Paper Spectral Geometry |
| Browse predictions | Observable Reference, 95 observables with formulas |
| Check proofs | Lean Formalization, 140-conjunct certificate |
Key Results
| Observable | K₇ Formula | Value | Exp. | Dev. |
|---|---|---|---|---|
| sin²θ_W | b₂/(b₃+dim(G₂)) = 21/91 | 3/13 | 0.2312 | 0.19% |
| N_gen | rank(E₈) − Weyl | 3 | 3 | exact |
| Q_Koide | dim(G₂)/b₂ = 14/21 | 2/3 | 0.6667 | 0.001% |
| α_s(M_Z) | √2/(dim(G₂)−p₂) | √2/12 | 0.1179 | 0.04% |
| δ_CP | dim(K₇)×dim(G₂)+H* | 197° | ~207-212° (NuFIT 6.1) | ~1σ |
| m_τ/m_e | 7+10×248+10×99 | 3477 | 3477.2 | 0.004% |
| Ω_DE | ln(2)×98/99 | 0.686 | 0.685 | 0.21% |
Exact Algebraic Relations
All predictions derive from topological constants of a compact G₂ manifold K₇ with Betti numbers b₂ = 21, b₃ = 77, coupled to E₈×E₈ gauge structure (dim = 496):
sin²θ_W = b₂ / (b₃ + dim(G₂)) = 21/91 = 3/13
Q_Koide = dim(G₂) / b₂ = 14/21 = 2/3
N_gen = |PSL(2,7)| / fund(E₇) = 168/56 = 3
κ_T = 1/(b₃ − dim(G₂) − p₂) = 1/61
α = e^K (geometric coupling, zero free params)
Falsification Tests
| Prediction | Experiment | Timeline | Status |
|---|---|---|---|
| δ_CP = 197° (window [182°, 212°]) | DUNE | 2028–2040 | Awaiting |
| sin²θ_W = 3/13 | FCC-ee | 2040s | Awaiting |
| N_gen = 3 (no 4th gen) | LHC/FCC | Ongoing | Consistent |
| m_s/m_d = 20 | Lattice QCD | ~2030 | Consistent |
Outreach
Accessible writing on the ideas behind K₇ lives on the Substack blog, in three tracks: The Series (physics through the games you have already played), The Ideas (why the constants might not be arbitrary), and The Story (an independent researcher, an AI, and a year of unorthodox research). The full list with French translations is in the Blog Index. Latest: The Constants of Nature Are Counts, the thesis and the date it can die, on one page.
Structure
This wiki consolidates K₇ documentation across three repositories:
- Arithmon/K7: Theoretical documentation, papers, outreach
- Arithmon/K7-Lean: Lean 4 proofs, Python package, blueprint
- Zenodo deposits: Archived data with DOIs
Browse the sidebar for full navigation, or see the Site Map for a complete index.
| *The K₇ Framework v3.5 | GitHub | Core | Blueprint | Zenodo (Paper A) · Paper B · Paper C | MIT License* |