Sym² Manifold Workbench
Given a set of seed points on a curve, the symmetric product Sym² maps every unordered pair (u, v) to a point in 3D: midpoint as x,y — distance as z. The seam (u = v) re-embeds the original curve at z = 0.
Free Open Demonstration
cuppcb.com is the free open demonstration of the PCB console and manifold engine — no account, no setup, runs in the browser.
NON LINEAR LANGUAGE — draw seed curves, reify Sym², run the PCB console, deploy friends. Open to anyone.
Demos
Standalone cartridge pages — each is a thin HTML shell loading the shared kernel plus a cartridge script that sets seeds, oracle, and heat behaviour.
Sym²(S¹) — 60 seed points on a circle, 1770 chords. Cyan cold material. The red seam IS the original circle re-embedded in 3D.
Open →Five curves lerp continuously — circle → star → figure-8 → rose-3 → heart. Material colour shifts with each shape.
Open →Sym²(two circles). Inner ring is heat source, outer ring is surface. Material lerps cold → lava in real time.
Open →Workbench
The main interactive kernel. Draw seed points on a canvas, the manifold rebuilds live. Use the PCB console to inject coordinates, run oracle expressions, connect to Frontier.
Docs
| Document | What it covers |
|---|---|
| Whitepaper | The math — Sym² construction, seam geometry, heat diffusion derivation |
| PCB reference | Console command dispatch, hello-world walkthrough, oracle scope variables |
| Design system | Colour tokens, typography, components — accessibility-first |
| kernel.js | Frozen shared runtime — manifold math, heat, Friends, PCB, render loop |