# YieldSpace

> An interest-rate market as a Uniswap v4 pool: the curve quotes a yield rather than a price, and converges to par at maturity on its own.

A production Uniswap v4 hook. Source: https://github.com/nirholas/yield-space. Part of the HookForge catalogue: https://hookforge.pages.dev

## How it works
A zero-coupon claim is worth less than the thing it pays out, by exactly the interest between now and maturity, and that discount shrinks to nothing as maturity arrives. Quote it on a constant-product curve and the curve does not know that. It prices the claim as a permanently distinct asset, so the pool's own convergence to par is something arbitrageurs have to impose on it, trade by trade, and the liquidity provider pays for every one of those trades. YieldSpace, from the Yield protocol's 2019 paper, is the curve that knows. It holds   x^(1 - t) + y^(1 - t) = k where `t` is the time to maturity as a fraction of a year. Far from maturity `t` is large, the exponent is small, and the curve is steep: a big discount, and the pool quotes a rate. As maturity approaches `t` goes to zero, the exponent goes to one, and the invariant becomes `x + y = k`, a constant-sum pool that trades one for one. The convergence is the curve, not an arbitrage opportunity, so nobody has to be paid to enforce it. The consequence for the provider is the whole point. On a constant-product pool, holding a maturing claim means being run over as it converges. Here the pool moves with it, so what the provider earns is fees on rate trading rather than a slow bleed to whoever noticed the calendar. `currency0` is the underlying and `currency1` is the claim on it. The pool's implied rate is published by {impliedRate}, in ray per year, which is the number this market is actually about.

## Prior art
The curve is the Yield protocol's YieldSpace (Niemerg, Robinson, Livnev, 2019), and Notional and Pendle ship relatives of it. All of them are their own AMMs. Bringing it to v4 as a custom curve, so a fixed-rate market is an ordinary pool that every v4 router, indexer and position manager already understands, is the contribution here; the maths is deliberately theirs.

## Where it does not help
The time term is clamped at one year, so a claim maturing further out than that is priced as if it matured in a year and the pool will quote it wrong until it comes inside the window. The pool also has no idea whether the claim is honoured: it converges to par because the clock says so, and if the issuer defaults the curve keeps confidently quoting par on a worthless asset. That risk belongs to whoever chose the pair.

## Facts
Slug: yield-space
Contract: YieldSpaceHook
Callbacks: none
Parameters: none
Dynamic fee required: no

## Caveats
- Unaudited.
- A deployment with status "deterministic" is a mined CREATE2 address with no code at it yet. Never present one as live.