Price discovery happens where the informed size trades. For most large, established assets that is the deep centralised venue, and the pool is a follower kept aligned by arbitrage — the benign form of extractable value, and the mechanism that makes a pool quote usable at all.
For a token that trades primarily or only on-chain, the pool is the price. Nothing is following anything; there is one venue and its quote is the market.
Why the distinction is practical
Because it decides what a divergence tells you. If the exchange leads, a pool trading away from it is mostly a statement about the pool: arbitrage has not closed it yet, because the size required is not worth the cost, or the depth is too thin, or fees make it uneconomic. That is a liquidity observation, not a market view.
If the pool leads, the same divergence is a market observation, because it is where the trading actually is.
Getting this backwards produces a specific, common error: reading a persistent pool premium on a thin token as bullish demand, when it is really the signature of a pool nobody can be bothered to arbitrage. The gap persists because closing it is not worth the price impact and fees, and it can persist for a long time without meaning anything.
What keeps them together
Arbitrage, and it is not free. An arbitrageur pays network fees, pays price impact on both legs, and carries inventory risk across settlement. Below some threshold the trade does not pay, and that threshold is the width of the band the two prices can sit apart in.
So the band is wider on a thin token, wider on an expensive chain, and wider when the pool is shallow — and the band itself is information about the token’s liquidity, quite apart from where inside it the price sits.
Reading it
Ask first where the size trades, then read the divergence in that light. And note that this is the same discipline as everywhere else in this series: two venues over one asset are two instruments, and a level in one is not a level in the other — the point made about books in IBIT is not Bitcoin.