Dots are orders in the order they arrived (a ring is a sell). The blue ring counts the batch's window of blocks; the black ring, how much of its cap is used. Once settled, each order shows the place it ran in.
Nobody knows who goes first.
CHRONOS is a Uniswap v4 pool that trades only in batches. Each batch runs in an order sealed by 268,435,456 squarings over RSA-2048, started only after the batch closes. No validator can finish them inside its 12-second slot, so nobody can put a trade in front of yours.
The last batch, in the order the delay chose
Above, the orders as they arrived. Below, the order they ran in. The red line went first.
Why nobody can choose
The order of a batch comes from a number that takes minutes of strictly sequential work to compute, and the work can only start once the batch is shut and the next Ethereum slot has been proposed. The proposer who shapes that slot has seconds to publish it; a machine twenty times faster than ours would still need longer than the slot to see where its block leads.