Quote from: albert0bsd on Today at 02:36:06 AM

How closely related can supposedly two "independent" UTXOs be if they share a common link buried deep within their ancestry?

If we make the assumption that addresses don't change hands, then all you can say is that maybe some part of those to UTXOs were owned by the same person a long time ago. I say maybe, because as soon as a transaction has more than one output, you cannot say "which" bitcoin ended up at which output, and indeed, such a concept does not exist at the protocol level.

The relevance of this is almost zero. Does it matter if both you and I both own coins that 10 years ago were both maybe owned by Mt Gox? Everyone will have handled cash at some point which was involved in a crime. What's that old statistic about 75% of bank notes having traces of cocaine on them?

Quote from: albert0bsd on Today at 02:36:06 AM

Is there some formula/equationor work already written on that?

Maybe. Blockchain analysis companies have their own black box of algorithms and equations which they use to create links between addresses and outputs, but as we were just discussing on another thread, it is anything but scientific and often wildly inaccurate: https://bitcointalk.org/index.php?topic=5464886.0

Quote from: albert0bsd on Today at 02:36:06 AM

I don’t know if this is a correct approach but I can't think of another way.

Here's a recent coinjoin transaction I just pulled: https://mempool.space/tx/54e5e265cad4a26bc64dd8ca439f0c62055d7e0a2ff3156f10166aeb17d631f8
Do we say that every output contains 12.5% of the coins of each input? Or do we say that each output contains 100% of the coins of one specific input, but we can only guess which input is linked to each output?

Both statements are wrong. At a protocol level there is no such distinction. So any guesses we make will be exactly that - guesses.

Quote from: albert0bsd on Today at 02:36:06 AM

Now, the question arises: When does an ancestor become insignificant or unrelated to a specific UTXO? I propose two options for consideration:

When it contributes less than a Satoshi of the Balance of the UXTO
When it contributes less than 547 Satoshis of the balance of the UXTO

I think the first question is "What are you trying to achieve?" We can clearly say that UTXO X is a great-great-great-great-.....-grandparent of UTXO Y, just by following the ancestry and ignoring the amounts. What are you trying to achieve by classifying this based on amounts? Some compliance mechanism? An inference of common ownership?