a theoretical series of transactions which move 100% of the existing bitcoin to some previously-unknown wallet address would reduce the BTCDD figure to 0%
You meant "increase the BTCDD to 100%". Your previous post in this thread was correct in this regard.
Even if you consider that there are lost coins, the theoretical BTCDD figure approaches zero as the number of days goes to infinity.
If there are lost coins and a finite total number of coins then the BTCDD percentage cannot possibly reach 100% ever.
If there are no more transactions then the BTCDD tends to 0%.
In the long run, if there are any transactions then the BTCDD has a lower bound given by the proportion of the transacted coins out of the total coins.
Arithmetically it seems to me that the percentage cannot exceed 50%: in fact it should reach 50% asymptotically.
Both statements are incorrect.
ByteCoin
OK, so I reversed 100% and 0%, you're absolutely right. But it seems like you realized that!
Sticking with the substance of the discussion: if the total transactions per day average 50% of the total coins outstanding over some longish period of time, then sure, it's asymptotic to 50%.
Let's do some math on that: assuming the BTC stabilizes at $5, the long term implication of the 50% asymptote is about 22M * $5 = $11M of Bitcoin transacted commerce per day or about $4B / year. That is 1/1000 the size of the VISA network at $4T/year, or about 0.1%. Not great. To reach 10% of the VISA network at a 50% asymtote, the network would require a BTC valuation of $100. It's not a bad goal!