One pool for any number of stablecoins. Concentrated liquidity that stays pegged, and isolates a single asset when it breaks peg. Derived from the Paradigm Orbital paper.
Three properties do the work. Tight execution at peg. Dense capital across N assets. And a clean fence when one of them breaks.
At peg, trades move along the sphere's flat equator. Every LP's tick concentrates liquidity where stables actually trade. Routes stay tight through the full depth of the book — not just the first few basis points.
price impact at peg, p=0.99 — measured against an equivalent flat-sphere pool.
price impact at peg, p=0.99
One dollar here behaves like ~154 in a flat sphere pool. Concentrated ticks compound across N assets in a single pool. No fragmentation across pairs, no idle reserves sitting outside the active range.
vs flat sphere, N = 5 — measured against an equivalent flat-sphere pool.
vs flat sphere, N = 5
When one asset breaks peg, the other N−1 keep trading. Ticks flip to their boundary and the broken asset is fenced off. The pool doesn't drain into the bad leg — healthy stables stay liquid against each other.
stay live through a depeg — measured against an equivalent flat-sphere pool.
stay live through a depeg
Three ideas do the work. A sphere for reserves. A plane for every position. A torus that holds them together.
The pool tracks a vector x ∈ ℝⁿ constrained to the sphere. The equal-price point sits on the surface; every swap walks along it.
Tight ticks give tight pricing and flip fast. Wide ticks back the pool up under depeg stress and only flip at the extremes.
Five aggregates — sumX, sumXSq, rInt, kBound, sBound — let mint / swap / burn check the invariant in constant time.
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