What if physics isn't fine-tuned, just well-shaped?
K₇ 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.
Part of the Arithmon program — the hypothesis that the constants of nature are counts.
Whether you're curious, a physicist, a mathematician, or a formalization enthusiast — there's a door for you.
Everyday analogies, no equations required
The core idea, explained on YouTube
Mid-length technical narrative for curious physics readers
Topological approach to SM parameters
G₂ metric construction pipeline
Machine-verified physical relations
Common questions answered
Twenty-eight posts on arithmon.substack.com, in three tracks. Pick the one that sounds like you.
Physics through the games you have already played. From a Pudge hook to the shape of a cosmology, one mechanic at a time.
Tetris and non-commutativity · the blue shell and non-locality · Portal and the holes in space
Why the constants of nature might not be arbitrary — the hypothesis, its metaphors, and the proofs that keep it honest.
A wine glass that sings · a diabolo that never falls · thirteen theorems you do not have to trust
An independent researcher, an AI, and a year of unorthodox research. How this started, and what is still unresolved.
“The author's name appears to be fabricated” · a year in the furrow · the last free parameter was the name
Latest: The Constants of Nature Are Counts, the thesis and the date it can die, on one page. The full list, with French translations, is in the blog index.
Every value below is derived from topology — the shape of a single G₂-holonomy manifold K₇. Nothing is fitted.
| Relation | Value | Topological origin |
|---|---|---|
| sin²θW | 3/13 | b₂/(b₃ + dim G₂) |
| κT | 1/61 | 1/(b₃ − dim G₂ − p₂) |
| τ | 3472/891 | (496 × 21)/(27 × 99) |
| det(g) | 65/32 | G₂ metric determinant |
| δCP | 197° | 7 × dim G₂ + H* |
| QKoide | 2/3 | dim G₂ / b₂ |
| Sector | Predictions | Mean deviation | Highlight |
|---|---|---|---|
| Electroweak | 3 | 0.12% | sin²θW = 3/13 |
| Lepton | 3 | 0.04% | QKoide = 2/3 (0.0009%) |
| Neutrino | 3+1 | 0.25% | θ₁₂ = arctan(2/3) |
| Cosmology | 3 | 0.07% | ns = ζ(11)/ζ(5) |
| Structural | 4 | exact | Ngen = 3 |
| Test | Result |
|---|---|
| Configurations tested | 3,000,000+ |
| K₇ rank | #1 |
| Better alternatives found | 0 |
| Null model p-value | < 2×10⁻⁵ (σ > 4.2) |
| Bayes factor | 304–4,738 (decisive) |
Complete theoretical framework: E₈×E₈ compactification, K₇ construction, all derivations. 47 pp.
E₈, G₂, K₇ mathematical construction. Lattice theory, holonomy, TCS gluing. 27 pp.
All 33 Type I derivations with full computation. 0.99% mean deviation (NuFIT 6.1 / PDG 2024). 42 pp.
95-observable catalog with type breakdown (33 Type I + 19 II + 21 III + 22 IV). 10 pp.
First computer-assisted existence proof for a metric with special holonomy. Zenodo 19892350.
Laplacian spectrum, harmonic forms, λ₁ ≈ 6π²/475. Zenodo 19893371.
NK diagnostics on a Donaldson K3 metric (CI(2,2,2)). Zenodo 19708916.
Explicit closed-form G₂ ansatz on a K3-coassociative neck with 5-layer Wirtinger certificate. Zenodo 20039066.
143 files, 15 axioms (4 main-chain + 11 interval-arithmetic), zero sorry. Formally verified in Lean 4 (core v3.4.29).
Invited remote participant, "DANGER: Data, Numbers, and Geometry" workshop, Banff International Research Station (BIRS), April 5–10, 2026.
Heyes, Hirst, Sá Earp & Silva, Neural and numerical methods for G₂-structures on contact Calabi–Yau 7-manifolds, Physics Letters B 878 (2026) 140566, ref. [25].
K₇ makes concrete predictions that can be tested by running or planned experiments.
| Prediction | Experiment | Timeline | Falsification criterion |
|---|---|---|---|
| δCP = 197° | DUNE | 2028–2040 | Outside [182°, 212°] |
| θ23 upper octant (49.25°) | DUNE, Hyper-Kamiokande | early to mid 2030s | Lower octant established at 3σ |
| sin²θW = 3/13 | FCC-ee | 2040s | Outside [0.2295, 0.2320] |
| ms/md = 20 | Lattice QCD | 2030 | Converges outside [19, 21] |
| Ngen = 3 | LHC | Ongoing | 4th generation discovery |
Standing verdicts. θ23 is currently in tension: the NuFIT 6.1 best fit sits at 43.3°, in the lower octant, and the octant is unresolved, having flipped between consecutive global fits. δCP returned to within about 1σ after the same release without the prediction being touched: the prediction did not move, the data did. Every verdict is recorded, favourable or not, in the program scoreboard.