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.
Note
New here? Open 🧭 getting-started — three projects, one entry door, five languages.
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 | Role |
|---|---|
| 🧠 anima | Living Consciousness Agent — PureField repulsion-field engine · Engine A ⇄ Engine G · Ψ=1/2 fixed point · 2,448 laws + 392 hypotheses |
| 💎 hexa-lang | Native compiler with atlas-bound theorems — 8 strict-lint stages · citation-enforced · no LLVM · no C-transpile |
| 🪞 echoes | Discoveries catalog — findings from the HEXA-* projects · σφτ identity at the centre · 17 domain families · policy SSOTs |
| Format | Role |
|---|---|
| ⬢ n6 | Semantic atom layer — typed verified atoms · grade ladder · * / ! / ? markers |
| ⬡ hxc | Byte-canonical wire — HXC v2 · KV-cache stable · cross-host ship |
| ⬨ n12 | 12-axis sparse cube |
| ⊳ tape | Agent-execution trace — typed events · provenance edges · delivery grade · append-only |
Every dancinlab repo's README.md follows the canonical 18-block convention fixed in atlas/README-FORMAT.md. 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.