1.  M. Friedman (1969), The Optimum Quantity of Money, Macmillan
  2. https://github.com/rmsams/stablecoins/blob/master/paper.pdf
  3.  This point depends largely on the specific assets chosen as collateral and the method of implementation and whether or not these assets were already being held for another purpose. We have in fact even written a cursory proposal suggesting this criticism can be circumvented.  
  4.  By introducing an additional third token, certain groups have attempted to conduct ICOs for such systems. While it is creative and occasionally profitable for the issuer, such a modification does nothing to improve upon the model and is more likely to prove detrimental. This is due to the fact that the third token exists merely to collect newly distributed coins in the event that their are no shares outstanding. Since we do not believe that there are any reasonable equilibrium states where such a scenario will occur, we perceive this third class of token to be merely a fundraising tool that may even weaken demand for shares.
  5. It follows from the simple fact that those with higher incomes can and do allocate a greater percentage of their incomes to financial assets that Seigniorage Shares will be disproportionately held by wealthier individuals. However, understanding this the analogous mechanism for fiat systems is slightly more involved. First, we must recognize that as household income increases so too does the income to debt ratio. Second, we note that the manipulation of interest rates is the primary method by which money supply is adjusted in fiat systems. Therefore, since those with higher incomes carry high debt loads, they are more directly affected by changes in monetary supply through interest rate manipulation. Moreover, as is the case with Seigniorage Shares, wealthy individuals are more likely to hold national bonds, which produce yields that closely track inflation. 
  6. The relationship between one's exposure to growth in currency supply and inflation can be understood as follows. As new money is issued into an economy, prices are driven up, or at least prevented from falling as they would have otherwise. While we can assume that everyone is equally exposed to this price increase, we other effects of new currency creation are not equally distributed. In the case of Seigniorage Shares, the additional currency issued serves to offset any losses incurred as a result of increasing prices for anyone holding shares. In fiat systems, it is the decreased cost of borrowing that serves to offset losses due to inflation. However, this offsetting benefit is distributed only according to one's debt level, which again is a function of one's income and wealth.
  7. It is important to note however, that the argument for rewarding individuals for taking increased risk only applies in the case of Seigniorage Shares and not in fiat systems since government bonds (at least in countries such as the US, Canada, EU, and UK) are considered "risk-free".
  8. The element of trustlessness is one of critical importance to the blockchain ethos and represents one of the core motives behind its creation and adoption.
  9. More specifically, Distributed Oracles suffer from the need for complex governance and dispute periods to protect against misbehavior by a minority group and lack of sufficient participation by the majority. On the other hand, Schelling Points are still largely theoretical and while they work well for extremely simple questions, determining price levels may still be beyond their scope.
  10. By non-financial transactions, we refer to all services and goods, excluding financial assets such as stocks, bonds, options, and currency instruments. We exclude financial transactions here to allow for the detection of financial crashes and asset bubbles. Exerting opposing pressure to which will be a critical task of the subsequent changes in Poly supply.
  11. Note that the velocity can be trivially extracted from our Protocol as specified in Protocol Requirement 2. More specifically, this could be measured directly by randomly selecting individual Polys, looking at how often they changed hands, and averaging the individual results.