How Does the Constant Product Formula ($x Y = K$) Enforce Price Parity with External Markets?

The constant product formula dictates that the product of the quantities of the two tokens ($x$ and $y$) must remain constant ($k$). When the price of one token changes externally, the pool's ratio becomes misaligned.

Arbitrageurs exploit this by trading until the ratio of $x$ to $y$ in the pool matches the external market price. This constant rebalancing mechanism ensures the pool's internal price tracks the external price, maintaining parity through incentives.