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Update: Cost comparison table
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bip-0442.md

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@@ -147,8 +147,8 @@ using `OP_PAIRCOMMIT`.
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One way to think about the 3 opcodes (`OP_CHECKSIGFROMSTACK`, `OP_INTERNALKEY`,
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`OP_PAIRCOMMIT`) is we decompose a `OP_CHECKSIGFROMSTACK` variant that can use
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a 1-byte `OP_TRUE` public key (substituting for the *taproot internal key*) and can
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commit to a number of stack elements as a message.
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a 1-byte `OP_TRUE` public key (substituting for the *taproot internal key*) and
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can commit to a number of stack elements as a message.
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### Behaviors LNhance tries to avoid introducing
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@@ -175,18 +175,20 @@ various reasons, either for expanding the scope or for unnecessary complexity:
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### Cost comparison of LN-Symmetry constructions
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| Method | ChannelS | UpdateSc | UpdateWi | 1-Update | 2-Update |
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| :------------ | -------: | -------: | -------: | --------: | --------: |
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| APO-annex | 2.25 vB | 28.25 vB | 25 vB | 305 vB | 461.5 vB |
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| APO-return | 2.25 vB | 28.25 vB | 16.5 vB | 338.5 vB | 528.5 vB |
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| CTV+CSFS+IKEY | 2.75 vB | 12.25 vB | 24.5 vB | 331 vB | 513 vB |
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| CTV+CSFS | 11 vB | 20.5 vB | 24.5 vB | 347.5 vB | 537.75 vB |
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| LNhance | 3 vB | 12.5 vB | 32.75 vB | 297.75 vB | 446.25 vB |
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| rekey | 7.25 vB | 16.75 vB | 73.75 vB | 347.25 vB | 541 vB |
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| Method | ChannelSc | UpdateSc | UpdateW | ForceC | Contest | Settle |
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| :------------ | --------: | -------: | ------: | ------: | ------: | :----: |
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| APO-Annex | 8 WU | 113 WU | 100 WU | 1221 WU | 627 WU | SigOp |
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| APO-Return | 8 WU | 113 WU | 66 WU | 1359 WU | 765 WU | SigOp |
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| CTV+CSFS+IKEY | 10 WU | 48 WU | 98 WU | 1328 WU | 732 WU | CTV |
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| CTV+CSFS | 43 WU | 81 WU | 98 WU | 1394 WU | 765 WU | CTV |
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| LNhance | 11 WU | 49 WU | 131 WU | 1191 WU | 594 WU | CTV |
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*ChannelSc: channel script, UpdateSc: update script, UpdateW: witness is the
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same size for both Force Close and Contest in LN-Symmetry, ForceC: total cost of unilateral close transactions*
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### Proving general computation
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Merkle trees can be used to prove out computation where the root of the tree
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Merkle trees can be used to prove computation where the root of the tree
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represents the *function* and the leaves represent the *inputs* and *output*.
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There are practical limits to the entropy space for the *inputs* as they need
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to be iterated over and hashed into a merkle root.

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