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Is it possible given on-chain and gossip protocol data to derive closing channel balances? For example, the following channel between ACINQ and magnetron has two txouts but unsure who's balance is which. Closed Channel Example

I know from Bolt #3 that transaction outputs are sorted by value in ascending order but is there something in the script to match closing balances to nodes?

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No, the ownership of the outputs of closing transactions is private. Nobody except the channel owners needs to know the final balances of the channel, so clearly it would be a privacy leak to serve this data unnecessarily.

You may be able to make an educated guess if one of the channel owners reuses the output to create another channel, or by analyzing the receiving wallets' fingerprints in order to guess per the software they might be using (e.g. the P2TR output here might be an indicator).

Note that a channel owners might not send the funds to their own wallet with the closing transaction.

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