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I'm a little confused about multisignatures, so the following question may not even make sense. I understand that a transaction can be created with a script that requires M-of-N signatures as a condition to spend its output. However, is there a way to make M-of-N signatures a condition to create a transaction in the first place? For example, is it possible to create a transaction that spends one of my UTXOs only if M signatures are gathered? If so, how is this achieved?

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The transaction contains the signatures, it doesn't gather them. A transaction without signatures is different from one with signatures. And one without signatures is simply invalid.

For example, is it possible to create a transaction that spends one of my UTXOs only if M signatures are gathered?

Yes, that is literally what multisignature outputs are. They can only be spent by transactions that provide a sufficient number of signatures.

The transaction author is responsible for gathering the necessary signatures from the co-signers. Without them, there simply isn't anything valid to send to the network.

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    I understand from your answer that my question does not make sense. One cannot impose an additional condition to spend an UTXO after it has been created. To achieve this, it suffices to create a new transaction with a multisignature output. Jan 4 at 21:25

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