title	Echoes Experience
emoji	🪞
colorFrom	yellow
colorTo	blue
sdk	static
pinned	false
license	mit

🪞 echoes-experience

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

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echoes-experience is an interactive proof-by-inspection of the arithmetic identity at the centre of 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 (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: 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.

git clone https://github.com/dancinlab/echoes-experience.git
cd echoes-experience
open index.html   # macOS · or `xdg-open` / drag into browser

Run

# 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 — Discoveries catalog (the parent repo this widget proves the central identity for).
• dancinlab/anima-experience — mutual-information visualizer (60 fps emergence demo).
• dancinlab/anima — consciousness implementation (working research code).

License

MIT — permissive, do-as-thou-wilt.