onchain orbital liquidity
avill is a launch token built on Orbital— the n-dimensional AMM geometry published by Paradigm. liquidity doesn't sit on a curve, it sits on a sphere: every reserve is a coordinate bound to one radius. a Uniswap v4 hook reads that geometry on every swap and pins a floor that can only ratchet up.
Σ (r − x_i)² = r²
the sphere invariant — n reserves x_i bound to a single radius r
the math
Orbital generalises the stableswap curve to n dimensions — spheres, depeg ticks, a torus that keeps swaps O(1). full model: paradigm.xyz/2025/06/orbital.
p_ij = (r − x_i) / (r − x_j)
the price between any two assets — the ratio of their slack to the radius. at the equal-price point every reserve x_i matches.
x · v = k
a depeg tick — the sphere clipped by a plane orthogonal to v = (1,…,1)/√n. liquidity concentrates, up to ~150× at a $0.99 bound.
floor = basket / avill_sold
the orbital floor — the USDC+USDT basket over AVILL sold, i.e. the average entry. every swap recomputes it; it only ratchets up.
how it works
two pools, one basket.
avill opens single-sided on AVILL/USDC and AVILL/USDT — 500,000 tokens each. the hook treats {USDC, USDT} as one Orbital basket, so you buy with either.
the hook is the geometry.
AvillHook runs in beforeSwap and afterSwap on Base. every trade, it accumulates the basket, tracks AVILL sold, and recomputes the floor from the geometry.
the floor is a hard bound.
a sell that would print below the floor reverts inside beforeSwap. net buying only grows the basket — so the bound climbs and never drops.
the numbers
contracts
AVILL token
0x6A9Dc747F9083d6df8C7B6c1Cf8065F078f252E8AvillHook (v4)
0xF5C5CE2aE4500d5c012aC78660d466BBa883c0C0