Good morning John Law,

> (at the expense of requiring an on-chain transaction to update
> the set of channels created by the factory).

Hmmm this kind of loses the point of a factory?
By my understanding, the point is that the set of channels can be changed 
*without* an onchain transaction.

Otherwise, it seems to me that factories with this "expense of requiring an 
on-chain transaction" can be created, today, without even Taproot:

* The funding transaction output pays to a simple n-of-n.
* The above n-of-n is spent by an *offchain* transaction that splits the funds 
to the current set of channels.
* To change the set of channels, the participants perform this ritual:
  * Create, but do not sign, an alternate transaction that spends the above 
n-of-n to a new n-of-n with the same participants (possibly with tweaked keys).
  * Create and sign, but do not broadcast, a transaction that spends the above 
alternate n-of-n output and splits it to the new set of channels.
  * Sign the alternate transaction and broadcast it, this is the on-chain 
transaction needed to update the set of channels.

The above works today without changes to Bitcoin, and even without Taproot 
(though for large N the witness size does become fairly large without Taproot).

The above is really just a "no updates" factory that cuts through its closing 
transaction with the opening of a new factory.

Regards,
ZmnSCPxj
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