#Clearing and d*

All orders in a batch trade at one discount, d*, chosen to match the most volume.

#Finding d*

For every tick k on the grid:

• D(k) is the size of all buys whose minimum discount is at or under k;
• S(k) is the size of all sells whose maximum discount is at or over k;
• the volume that could trade at k is min(D(k), S(k)).

The clear picks the k with the largest volume. Ties go to the smallest imbalance |D(k) − S(k)|; any tie left over is an interval, and d* is its middle, rounded toward the lower discount. A lone crossing pair therefore clears halfway between the two limits.

Because both sides are sized in SPACEX, d* depends only on the book, not on the oracle price. The Pyth price sets the level: price = P_SPCXx × (1 − d*).

#Who fills

Fills follow price priority:

• buyers fill from the lowest minimum discount up, since they bid the most;
• sellers fill from the highest maximum discount down, since they ask the least;
• the last tick touched on each side is shared pro rata by size.

Every order at a better tick than the marginal one fills in full. Orders past it get nothing.

#Rounding

Whoever receives rounds down and whoever pays rounds up, so the vault stays solvent in both assets after every settlement.

#Checking a clear yourself

Every batch page shows the revealed book as a histogram, the D(k) and S(k) curves, and d*. The page also recomputes the clear in your browser from the published histogram, with the same function the program mirrors, and shows whether it matches.