gift-framework/GIFT→Arithmon/K7The framework is now presented as the K₇ framework; K₇ remains the name of its founding phase. The move consolidates it under the Arithmon organisation alongside Atlas, Program, Lean and Sieve.
Nothing you cite will break. GitHub redirects the old URLs (web and
git clone/fetch/push), and the published papers citegithub.com/gift-framework/*: those redirects are load-bearing infrastructure, so the old paths will never be reused.One thing does not redirect: the documentation site moves from
gift-framework.github.io/K₇/toarithmon.github.io/K7/.Companion repository:
gift-framework/core→Arithmon/K7-Lean(moved 2026-07-14).
Part of the Arithmon program -- the hypothesis that the constants of nature are counts.
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: E₈×E₈ gauge theory compactified on a G₂-holonomy manifold K₇ with Betti numbers (b₂, b₃) = (21, 77).
The compact K_7 torsion-free existence theorem is an active analytic target,
not a completed theorem in this repository. Current status is tracked in
docs/analytic_status.md:
- Level E remains conditional on the anisotropic perturbation theorem
(J)and compact datum/topology wrappers. - Level Q has a Stage E certified D0 coefficient package.
- Level CF, a finite closed-form compact metric, remains a separate open programme.
Older public notes about Joyce or Donaldson should be read through that status ledger.
| Watch (8 min) | Read the blog |
| K₇ for Everyone | FAQ |
All posts on arithmon.substack.com.
| Post | Topic |
|---|---|
| Episode 4: The day Minecraft taught you to draw a sphere that wasn't one | Minecraft, discretization and the eternal problem of the continuum |
| The Furrow | One year of unorthodox research: what changed, what didn't, and what I still don't know |
| Episode 3: The day the blue shell knew where you were | Mario Kart, non-locality and correlations at a distance |
| No Word for This | Three names that don't work, and an open question about the role in human-AI collaboration |
| We've Released Our Draft Blueprint | Announcing K₇ v3.4 in plain language |
| Episode 2: The day Tetris taught you that order is everything | Tetris and productive non-commutativity |
| Episode 1: The day Newton lost control | Fall Guys and the myth of predictable physics |
| Episode 0: The day Pudge taught you quantum mechanics | Gaming as a school of quantum intuition (series opener) |
| Orientation, not ontology | The philosophical posture behind K₇ |
| What if the universe was a Lego set? | Counting pieces, recognizing themes, reading the manual |
| "The author's name appears to be fabricated" | Learning Physics with AI: the accidental origin of K₇ |
| 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 |
| Background | Start Here |
|---|---|
| Everyone | K₇ for Everyone -- Complete guide with everyday analogies |
| Overview | Executive Summary -- Mid-length technical narrative for curious physics readers |
| 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 |
Framework v3.5 (published: PDF, TeX, and markdown -- Zenodo 10.5281/zenodo.21296168)
| Document | Markdown | |
|---|---|---|
| Main Paper (47 pp.) | Markdown | |
| S1: Foundations | Markdown | |
| S2: Derivations | Markdown | |
| S3: Observables | Markdown | |
| S4: Sieve Diagnostics | Markdown |
LaTeX sources:
publications/papers/tex/. Archives:legacy/v3.4/,legacy/v3.3/.
| Paper | Description | DOI |
|---|---|---|
| A: Certified G₂ Structure (PDF) | First computer-assisted existence proof for a metric with special holonomy (TCS neck model) | 10.5281/zenodo.19892350 |
| B: Spectral Geometry (PDF) | Laplacian spectrum, harmonic forms, λ₁ = 6π²/475 | 10.5281/zenodo.19893371 |
| C: Newton-Kantorovich on K3 (PDF) | NK diagnostics on a Donaldson K3 metric (CI(2,2,2)) | 10.5281/zenodo.19708916 |
| D: Donaldson Analytic Note (PDF) | Explicit closed-form G₂ ansatz on a K3-coassociative neck with 5-layer Wirtinger certificate | 10.5281/zenodo.20039066 |
| E: Rank-1 Branched Adiabatic (PDF) | Neck-level analytic machinery closed at D₀ (open: (J) and H_global) | 10.5281/zenodo.21209413 |
| Parameters | Zero adjustable -- all structurally determined (3 integer primitives: N=3, r₈=8, r₂=2) |
| Verified | 15 Lean 4 axioms (4 on the prediction chain + 11 K3 interval-arithmetic certificates), zero sorry, 460+ certified relations (K7-Lean v3.4.29) |
| Parameter-free core | 33 exact relations among topological integers (Type I) -- each individually correct-or-wrong, none tunable |
| Falsifiable | δ_CP = 197°, N_gen = 3, θ₂₃ upper octant -- tested by DUNE / FCC-ee |
| Observables | 95 total (33 Type I + 19 Type II + 21 Type III + 22 Type IV); 66 with experimental data |
| Precision | 0.99% mean deviation on the 33 Type-I core relations (PDG 2024 / NuFIT 6.1 / Planck 2018) |
| Uniqueness | #1 of 3M+ random configurations tested (log₁₀ p_algebraic = −134) |
Dimensional reduction: E₈×E₈ (496D) → AdS₄ × K₇ (11D) → Standard Model (4D)
| 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 |
| 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 |
| Property | Value | Status |
|---|---|---|
| Associative 3-form | φ = (65/32)^{1/14} × φ₀ | EXACT local R^7 model |
| Metric | g = (65/32)^{1/7} × I₇ | EXACT local R^7 model |
| Torsion | T = 0 (constant form) | EXACT local R^7 model |
| det(g) | 65/32 | EXACT local R^7 model |
This table is not a compact K_7 torsion-free metric theorem.
| Metric | Value |
|---|---|
| Configurations tested | 3,000,000+ |
| K₇ rank | #1 |
| Mean deviation | 0.99% on the 33 Type-I core relations (NuFIT 6.1) |
| Better alternatives found | 0 |
| 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% |
| 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
| Prediction | Experiment | Timeline | Falsification Criterion |
|---|---|---|---|
| δ_CP = 197° | DUNE | 2028-2040 | Outside [182°, 212°] at 3σ |
| 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 |
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.
| Repository | Description |
|---|---|
| Arithmon/K7-Lean | Formal verification (Lean 4), K₇ metric pipeline, giftpy (formerly gift-framework/core) |
| Platform | |
|---|---|
| Substack | arithmon.substack.com |
| YouTube | @arithmon |
| X | @ArithmonProgram |
| Archive | |
|---|---|
| Zenodo (framework v3.5, current) | 10.5281/zenodo.21296168 |
| Zenodo (framework concept DOI, always latest) | 10.5281/zenodo.16891489 |
| Zenodo (framework v3.4 archive) | 10.5281/zenodo.20070101 |
| Zenodo (framework v3.3 archive) | 10.5281/zenodo.18837071 |
| Zenodo (Paper E, rank-1 branched adiabatic) | 10.5281/zenodo.21209413 |
| Zenodo (Paper A, certified G₂) | 10.5281/zenodo.19892350 |
| Zenodo (Paper B, spectral) | 10.5281/zenodo.19893371 |
| Zenodo (Paper C, K3 NK) | 10.5281/zenodo.19708916 |
| Zenodo (Paper D, Donaldson analytic) | 10.5281/zenodo.20039066 |
| ResearchGate | Author page |
@software{k7_framework,
title = {The K₇ Framework (formerly GIFT)},
author = {de La Fournière, Brieuc},
year = {2026},
url = {https://github.com/Arithmon/K7},
doi = {10.5281/zenodo.16891489},
version = {3.5}
}See CITATION.md for additional formats.
MIT License, see LICENSE
Gift from bit
K₇ is the founding framework of the Arithmon program.