This proposal appears to be flawed, unless I am missing something. I have only read the first 4 pages thus far.
1. You propose to decrease the coin rewards as coin-days-destroyed volume increases, so this makes it less costly for an attacker to obtain > 50% of the hash rate assuming the attacker includes all the transactions. You apparently are attempting to imply there is no useful attack to do if the attacker is including the most coin-days-destroyed? Please confirm or deny then I will dig into more analysis of this vector.
2. Also how do you choose between someone who generates a proof-of-work hash with lower coin-days-destroyed several times sooner than the network propagation delay versus another who generates it that much delayed with a higher coin-days-destroyed? If you choose the latter, then you've killed the proof-of-work incentive because it means it will always pay to be later and wait for more transactions to arrive.
3. You claim to defeat my Transactions Withholding Attack, by blacklisting those who send blocks with transactions that were not recently seen by all miners. I
retorted against this recently. This centralizes the network (all for one and one for all outcome) by requiring every miner to be responsible for the incoming network connectivity of other miners. And it centralizes the network in other ways, such it can't tolerate a temporary partitioning of the network due to connectivity outages.
P.S. By coin-days-destroyed, I assume you mean coin value x days, otherwise you would motivate proliferation of dust.
After some consideration I have decided to replace proof-of-work all together and use transaction fees to regulate block production. A new block is produced once enough transaction fees have been accumulated. The node that generates the transaction with sufficient fees broadcasts it. Ultimately all that matters is that the network reaches consensus and orphans are no issue. Nodes in the network can even stop propagating new blocks for a couple of minutes after the previous block. If transactions are coming to quickly I simply up the transaction fee like you would adjust the difficulty in BTC. These fees are then destroyed to pay dividends rather than paid to a miner.
As a result it doesn't matter how much hash power you have because you must *pay* to submit a block and the best-fit block is the one with the most coin-days destroyed so even if you pay to submit a block with no transactions, it will be rejected.
3. Does not centralize the network, it is a local calculation performed by all nodes relative to their peers.
Yes, coin value * days.
Quoting this very important historical event, so it can't be deleted.