How it works: the sphere

Why a sphere

A stablecoin pool wants two things: keep prices near 1:1 when everything's healthy, and hold up when something breaks. Orbital's insight is to put the reserves of all n stablecoins on a single n-dimensional sphere. The pool's state is one point on that surface; a trade slides the point along it. Because every stable shares one surface, there's one deep pool instead of n·(n−1)/2 shallow pairs.

At the balanced point (all reserves equal) every pair prices at 1:1. As you trade one stable in, its reserve rises and its price drifts down — the same restoring behavior a good stableswap has, generalized to n dimensions.

Ticks: concentrated liquidity in n dimensions

Uniswap V3 let LPs concentrate liquidity in a price range. Spherra generalizes that to the sphere: an LP adds liquidity at a depeg parameter p (between 0.5 and 1), which defines a tick — a band of the sphere near the peg where their capital is active. Concentrating near peg means the same dollars provide much deeper liquidity where stables actually trade, so spreads are tighter and execution is better.

A tick is either interior (active, on the trading surface) or boundary/bound (its plane has been crossed). As a trade pushes far enough, it crosses tick planes — those crossings are computed exactly and are part of why the swap math had to be proven, not just tested.

A trade is a slide along the surface

When you swap tokenIn for tokenOut, the pool solves for the largest output that keeps the reserve point on the sphere (the torus invariant F ≤ 0, pool-favorable rounding). Large trades cross more tick planes and get more price impact — exactly the slippage you'd expect, emerging from the geometry rather than a hand-tuned curve.

You can feel all of this — swaps, slippage, tick crossings, and the depeg quarantine — in the interactive simulator. (The simulator runs a simplified single-sphere model for intuition; the production engine adds the full tick/torus machinery and is the one that's formally verified.)

The invariant

The pool's health signal is the torus residual F. Committed states keep F ≤ 0 (within a tiny, calibrated tolerance) — the pool is always on or inside its sphere, i.e. solvent. This is the same invariant that's proven in Lean and fuzzed after every call, and the same F the dapp shows as an "in band ✓" health pill.