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Here are the scripts found in BOLT 03.

Offered HTLC Outputs:

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2nd stage output script:

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Why not just use one pubkey, like localpubkey?

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The split is intentional, and allows for trustless watching of revoked transactions, which is often outsourced with the help of watchtowers.

From Bolt3

Splitting the local_delayedpubkey, which is required for the penalty transaction, allows it to be shared with the watcher without revealing localpubkey; even if both peers use the same watcher, nothing is revealed.

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