it is very difficult to form a 51% attack to obtain any significant share of the 10 billion fee based transactions daily, especially when one is trying to manipulate a massive amount of transactions in a 1-year sliding window.
Proof-of-transaction incentivizes users from an early stage to join a harvest club with the most harvest power. Because of this, it is unlikely that by the year 2040 there will be several thousand separate harvest clubs, as it is likely that one of the early large harvest clubs will become a majority pool, sucking up most of the new users that enter the network. In my estimation, by 2040 there will only be a few very large harvest clubs.
Potential resolution: Limit the number of members per harvest club to ~5,000.
Potential resolution 2: Require a physical authenticator for transactions.
Therefore, holders transfer numerous coins among own addresses will have to pay attractive fees to be recogonized. These fees collected by miners will be distribute to club members according to the history transaction weight or transaction fee weight.
I notice that later you state that you'll be using weighted transaction fee, rather than relative transaction number to determine the odds of who gets to mine the new block and receive the reward. However, this does not resolve the Sybil attack, it simply changes the nature of the attack. You assume that the the purpose of the sybil attack is to manipulate the network for financial gain, however, it can also be used to discredit the worth of the TAU blockchain and poison it from within. For example, if a bad actor with particularly deep pockets were to exclusively send high fee transactions in the scope of the 1-year window, then he would have the greatest chance of mining the new block. If the discrepancy between the transaction fees of the bad acting harvest club, and average harvest club is high enough, then they could mine and perhaps manipulate a significant fraction of the market, producing a situation where small, or poorly funded clubs simply cannot compete, and reducing the utility of the TAU blockchain for these individuals. A sudden increase in the transaction fees of one of the larger harvest clubs would also
Potential resolution: Limit the rate of change possible between the largest harvest clubs to ensure no club can suddenly (out-fee) the rest of the network.
We found potentially using transaction fee accumulation in the transaction pending pool to replace the time element and let size to be adjustable seems to achieve ideal scalability on chain.
Why not just fix the scaling to the relative change in transactions each month, or three months? And the relative change in the number of miners on the network.
For example if there was a 50% increase in number of transactions (A) in a 1 month period, and 50% increase in number miners (B), then there will be no scaling required. However, if either side of this is unbalanced (A /= B), then the percentage of block size increase can be calculated as A / B, if the number is below 1, then the block size is scaled down proportionally, if it is above 1, then it is scaled up proportionally
You also mention that TAUcoin is the fairest blockchain because it uses normal transactional activity in order to determine who has the highest chance of mining the next block and hence receiving their deserved fraction of the reward. However, this doesn't truly fit the definition of fair, as TAU essential inherits the biases in the users spending power. For example, a wealthy user and a poor user both start using TAU for their daily activities, the wealthy user is able to send more transactions as they have more disposable income and can afford to pay higher fees, whereas a poorer user will typically make fewer transactions, of smaller size and hence smaller fee. This system is therefore biased towards high net worth and high spending individuals.
Potential resolution: Rather than using simply the velocity of money as the main determinant of harvesting power, instead implement a second associated measure called transaction power. High power transactions would be those sent between high fee harvest clubs, and can hence be associated with high net worth. The true harvest power would be a ratio between the transaction power and transaction velocity, with transaction power acting to reduce harvest power, and transaction velocity acting to increase it. Though, overall this might incentivize network spam with low fee transactions.