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It simply sends hashable work to the chip itself - called a midstate - that can be hashed 4 billion times.
Pool sends a stratum work base with the merkle slice, no transactions, and not the full merkle tree (about 1350 Bytes).
Miner 'generates' a coinbase transaction and then builds a block header.
Miner hashes that to a midstate, then sends that to the chips. (Edit: this is the USB step)
Transactions have nothing effectively to do with stratum, since that's way too much network and way too much overhead.
With transactions, the data per work change would be between 2MB and 8MB
This was called 'GBT' years ago and no one used it for the obvious reason, miners can't handle that much data and work,
and no one ever implemented a transaction selection on top of that - that only produces a biased network, which is a very bad idea.
Kano,
Can you point to any documentation on how BTC pool mining actually works?