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How are Satoshis accounted for and transferred? As in, is it the case that when I have ownership of a particular Sat at an address, is it actually that I own sat number 241536 from BitCoin number 237518 or whatever?

Are Sats connected to a particular Coin in that manner or are they separate and just that when I have ownership of 100,000,000 Sats I can say I have the equivalent of a full bitcoin?

I realise they may seem like a supper silly question but it has been bothering me.

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Satoshis, or BTC, are not explicitly tracked. You cannot compute an exact history of the addresses a specific satoshi has passed through.

At a technical level, every transaction "mixes" a number of inputs (each of 0 or more satoshis) into a number of outputs (again, each of 0 or more satoshis). Typical transactions have 1 or a few inputs and 2 outputs, though any non-zero number of inputs and outputs is possible. If a transaction has exactly one input and exactly one output, you can might be able to say the satoshis "pass through", but in any other case, they get split and merged by every transaction, and you can't say which one goes where - they all go everywhere.

At best, you can compute a "history" of a transaction output, by enumerating all addresses/scripts any of of its ancestor coins have passed through. For most outputs, I imagine that a substantial portion of the entire chain's history will be included in that ancestor set, though.

Also, be aware of techniques like CoinSwap, where two parties can "swap" ownership of coins, without there being any on-chain evidence linking the two coins.

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Units of measure

Satoshis and Bitcoin (BTC) are mainly a unit of measure. 100,000,000 Satoshi is the same magnitude as 1 Bitcoin just as 100 US cents is the same magnitude as 1 US Dollar.

A bitcoin wallet or other software might display the amount in Bitcoin or in some other units instead of in Satoshi. This is just a choice of presentation. Just like you might write down 5 cents as $0.05 or as ¥5.7 or €0.043 (at today's exchange rate). Writing it down any of these ways doesn't change the nature of the actual 5 cent coin in your pocket.

The Bitcoin network keeps track of money as amounts using only Satoshi as it's unit of measure. The list of "coins" is a list of unspent transaction outputs (UTXOs) derived by processing the list of Bitcoin transactions that acts as a transaction journal and which is replicated by each bitcoin node.

when I have ownership of 100,000,000 Sats I can say I have the equivalent of a full bitcoin?

Yes, just as when your pocket contains five US quarters, a nickel and a dime, you can say you have one dollar forty. A similar approach can be taken for Bitcoin amounts or for any currency really. You can express a total without enumerating the coins.

ID or serial numbers for coins?

is it actually that I own sat number 241536 from BitCoin number 237518 or whatever?

The coins are identified by the hash of the transaction that created them and their position in the list of outputs of that transaction.

However, Transactions destroy coins. Every transaction effectively melts down all coins that are input to the transaction, stirs the molten metal thoroughly and then casts a set of completely new coins for the outputs of transactions.

Note that Transactions don't link old coins to new ones individually. All input coins are destroyed and do not have any individual link to specific newly created coins.

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