I made a comment on
https://github.com/bitcoin/bips/pull/943#issuecomment-876034559 but it
occurred to me it is more ML appropriate.

In general, one thing that strikes me is that when anyprevout is used for
eltoo you're generally doing a script like:

    10 CSV DROP
    1::musigkey(As,Bs) CHECKSIG
    <S+1> CLTV DROP
   1::musigkey(Au,Bu) CHECKSIG

This means that you're overloading the CLTV clause, which means it's
impossible to use Eltoo and use a absolute lock time, it also means you
have to use fewer than a billion sequences, and if you pick a random # to
mask how many payments you've done / pick random gaps let's say that
reduces your numbers in half. That may be enough, but is still relatively
limited. There is also the issue that multiple inputs cannot be combined
into a transaction if they have signed on different locktimes.

Since Eltoo is the primary motivation for ANYPREVOUT, it's worth making
sure we have all the parts we'd need bundled together to see it be

A few options come to mind that might be desirable in order to better serve
the eltoo usecase

1) Define a new CSV type (e.g. define (1<<31 && 1<<30) as being dedicated
to eltoo sequences). This has the benefit of giving a per input sequence,
but the drawback of using a CSV bit. Because there's only 1 CSV per input,
this technique cannot be used with a sequence tag.
2) CSFS -- it would be possible to take a signature from stack for an
arbitrary higher number, e.g.:
    10 CSV DROP
    1::musigkey(As,Bs) CHECKSIG
    DUP musigkey(Aseq, BSeq) CSFSV <S+1> GTE VERIFY
   1::musigkey(Au,Bu) CHECKSIG
Then, posession of a higher signed sequence would allow for the use of the
update path. However, the downside is that there would be no guarantee that
the new state provided for update would be higher than the past one without
a more advanced covenant.
3) Sequenced Signature: It could be set up such that ANYPREVOUT keys are
tagged with a N byte sequence (instead of 1), and a part of the process of
signature verification includes hashing a sequence on the signature itself.


    10 CSV DROP
    1::musigkey(As,Bs) CHECKSIG
   <N>::musigkey(Au,Bu) CHECKSIG
To satisfy this clause, a signature `<N+1>::S` would be required. When
validating the signature S, the APO digest would have to include the value
<N+1>. It is non cryptographically checked that N+1 > N.
5) Similar to 3, but look at more values off the stack. This is also OK,
but violates the principle of not making opcodes take variable numbers of
things off the stack. Verify semantics on the extra data fields could
ameliorate this concern, and it might make sense to do it that way.
4) Something in the Annex: It would also be possible to define a new
generic place for lock times in the annex (to permit dual height/time
relative/absolute, all per input. The pro of this approach is that it would
be solving an outstanding problem for script that we want to solve anyways,
the downside is that the Annex is totally undefined presently so it's
unclear that this is an appropriate use for it.
5) Do Nothing :)

Overall I'm somewhat partial to option 3 as it seems to be closest to
making ANYPREVOUT more precisely designed to support Eltoo. It would also
be possible to make it such that if the tag N=1, then the behavior is
identical to the proposal currently.

@JeremyRubin <https://twitter.com/JeremyRubin>
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