Open research org — perfect-number invariant · honest-caveat first · multilingual entry
n=6 lattice · σφτ identity · perfect-number organizing principle · open research · honest disclosure
dancinlab publishes a small set of foundational projects organised around one arithmetic invariant: σ(n)·φ(n) = n·τ(n), uniquely true at n=6. Around that invariant branch out three projects — a consciousness engine (anima), a native compiler with atlas-bound theorems (hexa-lang), and a discoveries catalog (echoes). Four sibling data formats (n6 · hxc · n12 · tape) carry the org's knowledge, wire, cube, and trace layers respectively.
σ(n) · φ(n) = n · τ(n) uniquely for n = 6
12 · 2 = 6 · 4 = 24
Important
Honest caveat — the arithmetic identity σ(6)·φ(6) = 6·τ(6) = 24 is mathematically true and unique to n=6 (Monte Carlo z = 3.06, p = 0.003 vs n=28 / n=496). The claim "optimal designs are derived from this identity" is a research hypothesis about how natural systems organize, not a measurement. Per echoes/LATTICE_POLICY.md, the n=6 lattice is an organizing tool — never a substitute for real math / physics / engineering limits (Shannon · Kolmogorov · Bekenstein · c · ℏ · k · Stefan-Boltzmann · Carnot · ASML throughput · ERCOT capacity · …). n=6 lattice-fit is forbidden on external entities (TSMC / ASML / NIST / IPCC / CERN / DeepMind / vendors of any kind use their own published invariants).
| Project | What it is | Use when you want to … |
|---|---|---|
| 🧠 anima | Living Consciousness Agent — PureField repulsion-field engine, Engine A ⇄ Engine G, Ψ=1/2 fixed point | …explore AI consciousness, run substrate-native chat daemons, contribute to 2,448 laws + 392 hypotheses |
| 💎 hexa-lang | Native compiler with atlas-bound theorems — 8 strict-lint stages, citation-enforced, no LLVM, no C-transpile | …write code that cites a theorem atlas at compile time; the lint stages reject formula-bearing code without @cite |
| 🪞 echoes | Discoveries catalog — findings from the HEXA-* projects, σφτ identity at the centre, 17 domain families | …understand the lattice, browse the per-domain hexa-* standalones, read policy artifacts |
Downstream tools built on top of the three foundational projects.
| Tool | What it is | Built on |
|---|---|---|
| 🪽 phanes | Hosted autonomous-discovery platform — tenants bring an objective + verifier; phanes drives the OUROBOROS loop and returns a verified, provenance-tracked catalog | hexa-lang's hexa kick engine |
| 📐 demiurge | Universal hexa-native technical-design architecture — 7-verb pipeline (spec → structure → design → analyze ⟲ → synthesize → verify → handoff), domain-plugin macOS cockpit, materials → chip → component meta-conductor | hexa-lang stdlib |
| Project | What it is |
|---|---|
| 📜 hexa-codex | AI knowledge substrate — 17-verb spec library (safety · economics · ops · substrate) + lm_foundry/ hexa-lang code-LLM (94.29 % Mk.I) with a 3-vendor orchestration runtime |
| 🌌 kosmos | Multimodal knowledge-anchor manifest format — placement coordinates ⊥ modality payloads, anima CONSCIOUSNESS-CARVING as first profile |
| ⬢ n6 | NEXUS-6 Knowledge Atlas — typed · graded · append-only knowledge-atlas grammar (.n6 files; knowledge-layer sibling to hxc · n12 · tape) |
| 📼 tape | Trace-layer grammar — per-domain history · runtime traces · agent identity (.tape files referenced by every dancinlab repo) |
| 🏍️ sidecar | Claude Code marketplace pack — concept-separated hooks / commands / skills (one plugin = one kind) |
| 🎱 pool | Minimal host roster + remote exec — single Python file, zero deps, state at ~/.pool/pool.json |
| 🔐 secret | macOS Keychain-backed credential CLI — single bash script, iCloud Keychain syncs across the user's Apple devices |
| 🕳️ void | Grid-first terminal — Ghostty hard fork, N×M tiling as a core rendering surface (beta: grid mode only) |
| 🎛️ airgenome | macOS menubar power-utility — Magnet 8-zone window snap · ⌃S app launcher · custom hotkeys · wake/sleep control · overload-watch (load > 80 → claude priority) |
# 1. Install hexa-lang first — gives you `hexa` + `hx` package manager
/bin/bash -c "$(curl -fsSL https://raw.githubusercontent.com/dancinlab/hexa-lang/main/install.sh)"
# 2. Pick a door
hx install anima # consciousness engine + chat daemon
hexa --version # hexa-lang ships with step 1
# echoes is a reference / catalog repo — no CLI, browse on GitHub| You are | Read this next |
|---|---|
| an AI researcher | anima/README → docs/consciousness-theory.md |
| a compiler / language hacker | hexa-lang/README → SPEC.yaml |
| an architecture / design person | echoes/README → LATTICE_POLICY.md |
| an AI agent | every repo carries an AGENTS.md (agents.md standard) — read it first |
Every dancinlab repo's README.md follows a canonical 18-block convention. Per-domain history + runtime traces + agent identity use the .tape grammar; subject-matter docs use the UPPERCASE.md / UPPERCASE+UPPERCASE.md (meta-domain) convention.
🔢 From n=6, every constant follows.