We both valued our respective sats at some defined value X
There is no single X, value is subjective, but that's an aside.
This would be an instance of inflation [...]
That's a convoluted way to look at it. It's just an increase in precision. More decimal places. Like expressing the length of something as an integer number of metres. If you need more precision, you go to millimetres. So if your backyard was measured to be 35 m long, if you measure it in mm precision you may discover it's actually 34.983 m or 35.112 m long. Of course it doesn't inflate anything. In implementation, if BTC amounts are expressed as 64 bit ints (in fact, I reckon only 51 bits are needed), this could be increased to 128 bits if mankind and Bitcoin survive for long enough.
There is no single X, value is subjective, but that's an aside. This just seems petty at this point. The whole point of the construction is under the assumption we (subjectively) valued satoshis at some exchange rate with something else. Like 2 people both valuing a sat as a loaf of bread. Yes, obviously individuals can value their sat at $1m if they choose. It has nothing to do with my point.
That's a convoluted way to look at it. It's just an increase in precision. More decimal places.
It's not convoluted, it's simple actually. Multiplying the value of sats does allow you to increase the precision, but whether we rename the basic units to something like millisatoshis or keep calling the base unit sats doesn't matter.
And yes in the implementation Bitcoin amount are expressed as 64 bit integers. 51 bits were not used in the amount.
The main point is that it doesn't matter whether you keep the unit in satoshi and multiply everyone's supply equally or to multiply and change the base unit to millisatoshis. Everyone should still consider the value of their satoshis to be the same as before.
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It does matter. You can multiply by a power of 10 in the implementation, to stick to integer representations.
But it's a terrible idea to expose that change to humans at the nominal level, because, unlike the code, it results in countless references to update. And messes with their minds unnecessarily.
Let's say I bought 1 BTC and made a blog post about it. Now, after the split, I own 10 "new BTC", but someone reading the blog will read that I bought 1 BTC and won't know whether it refers to new or old BTC -- unless I update the blog post to clarify that.
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