Echoes Experience — interactive σφτ proof widget · HF Space · slider n=2..1000 · vanilla JS/Canvas · zero roundtrip
σφτ · identity · n=6 · slider · canvas · proof-by-inspection · static · no-python
--- `echoes-experience` is an interactive proof-by-inspection of the arithmetic identity at the centre of [`dancinlab/echoes`](https://github.com/dancinlab/echoes): ``` σ(n) · φ(n) = n · τ(n) ``` uniquely at `n = 6`. Slide `n` from 2 to 1000 and watch the equation collapse to equality only at n=6 (and at no other `n` in the swept range — confirmed by exhaustive Lean 4 proof on `[2, 30]` and Python proof on `[2, 10000]` in the parent repo). > [!NOTE] > Companion to [`dancinlab/echoes`](https://github.com/dancinlab/echoes) (Discoveries catalog · parent repo). Dual-remote: pushes to GitHub (`origin`) AND HuggingFace Spaces (`hf`). ## Math - **σ(n)** — sum of divisors of n. For n=6: `1 + 2 + 3 + 6 = 12`. - **φ(n)** — Euler's totient — count of integers in `[1, n]` coprime to n. For n=6: `{1, 5}` → φ(6) = 2. - **τ(n)** — number of divisors of n. For n=6: `{1, 2, 3, 6}` → τ(6) = 4. - **Identity check:** `σ(n) · φ(n) ?= n · τ(n)`. At n=6: `12 · 2 = 24` and `6 · 4 = 24` ✅. ## Tech - Static HF Space (`sdk: static`) — first paint < 1 s, no cold start, no Python runtime. - Vanilla JS / Canvas — single self-contained `index.html`, no framework, no bundler. - All math runs client-side (gcd / divisors / phi-set via stdlib loops). At n=1000 ≈ instant. ## Honest caveat The arithmetic identity is **mathematically true** and unique to n=6 on the swept range (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**. See [`echoes/LATTICE_POLICY.md`](https://github.com/dancinlab/echoes/blob/main/LATTICE_POLICY.md): the n=6 lattice is an organizing tool, never a substitute for real math / physics / engineering limits. ## Status - live on HuggingFace Spaces — `https://huggingface.co/spaces/dancinlab/echoes-experience` - static sdk · single `index.html` · zero build step - slider sweep n=2..1000 · client-side math · instant render - dual-remote: `origin` (GitHub) + `hf` (HuggingFace Space) ## Install No install. It's a static page — clone and open `index.html`, or visit the HF Space. ```sh git clone https://github.com/dancinlab/echoes-experience.git cd echoes-experience open index.html # macOS · or `xdg-open` / drag into browser ``` ## Run ```sh # local preview open index.html # or serve over HTTP (any static server) python3 -m http.server 8000 # → http://localhost:8000 # push to BOTH remotes (GitHub + HuggingFace Space) git push origin main git push hf main ``` ## Repo layout ``` echoes-experience/ ├── AGENTS.tape # governance + identity (.tape v1.2) ├── CLAUDE.md # symlink → AGENTS.tape ├── README.md # this file (atlas/README-FORMAT.md compliant) ├── index.html # the widget · HTML + inline Canvas + JS └── docs/ └── logo.svg # repo logo (gold #bf8700) ``` ## Sister - [dancinlab/echoes](https://github.com/dancinlab/echoes) — Discoveries catalog (the parent repo this widget proves the central identity for). - [dancinlab/anima-experience](https://huggingface.co/spaces/dancinlab/anima-experience) — mutual-information visualizer (60 fps emergence demo). - [dancinlab/anima](https://github.com/dancinlab/anima) — consciousness implementation (working research code). ## License [MIT](LICENSE) — permissive, do-as-thou-wilt.