SAX's Modified Bonding Curve

Combining the Bancor Bonding Curve with Virality Co-efficient to calculate a trend's price movements.

Calculate The Buy Price Of A Trend

In the integration of the Bancor Bonding Curve with the Virality Co-efficient, the calculation of the buy price for a nib (unit of a trend) becomes a dynamic and multifaceted process. Initially, the current supply of the trend, denoted as 'x', is used as input in the standard Bancor Bonding Curve formula to determine the base price of the trend.

This formula, based on the relationship between the trend's supply and price, gives a foundational valuation. Next, the potential future supply, represented as 'x + 1', is considered to calculate what the price would be if an additional nib were to be bought, essentially predicting the next step on the bonding curve. The difference in price between these two points (the 'delta') represents the price impact of purchasing one additional nib of trend.

This delta is then modified by the Virality Coefficient, a factor that scales the price change based on the social media engagement and popularity associated with the trend, measured through metrics like retweets, comments, and favorites on specific hashtags. The final buy price is then obtained by adding this adjusted delta to the original price at supply 'x', thereby reflecting both the mathematical framework of the bonding curve and the real-time social sentiment captured by the Virality Co-efficient.

This method ensures that the trend's price not only adheres to the principles of supply and demand but also dynamically responds to its perceived value and popularity in the broader social media landscape.

Calculate The Sell Price Of A Trend

Whenever a sale is contemplated, an integer from 1 to n is assigned to each outstanding nib of the trend. The amount nibs to be sold will be assigned the highest numbers, n-1, n-2, etc. What this does is it gives the highest weight to first sellers, and as a result, the highest bid prices for the trend. This is done to balance the Bid price as close to the Ask price, since the Virality Coefficient changes and thus causes Ask prices to change. If the Virality Co-efficient changes, Ask prices cannot be static.

To calculate the selling price, we first determine the size of the asset pool (sum of all purchases) for the particular hashtag. Once this is done, we look at the current Buy Prices for the number of nibs outstanding using the current Virality Co-efficient. At each nib's interval, a percentage weight based on price only is assigned. This percentage weight is then multiplied by the size of the asset pool, resulting in a Sell Price that will not bankrupt the system, no matter how high the Virality Co-efficient becomes.

For example: Say the total asset pool for this trend is 2 USDB, and only two nibs (units) of trends are outstanding, there will be two buy prices using the current Virality Co-efficient. Since the total supply is 10,002 (10,000 initial supply + 2 nibs outstanding) with an initial price of 0.01, assuming the Virality Coefficient = 10, the current buy price of a nib (one unit of a trend) is 0.0110002. Then let's calculate the Percentage Allocation of the 2 nibs of trends. Nib 1 is assigned number 1 and nib 2 is assigned number 2 for the selling sequence. The total sum is 3, nib 1 makes up 33.33% (1/(1+2)), and nib 2's weight is 66.66% (2/(1+2)). Then we multiply those weights by the total asset pool of 2 USDB. Nib 1's Sell Price will be 0.66 USDB and Nib 2's will be 1.33 USDB. Since we will take the lesser of the Buy Price or Percentage Allocation calculation to decide the Sell Price, we default to use the Buy Price of 0.0110002 as the current Sell Price of 1 nib of trend.

SAX's Formulas:

• Buy Price = [(New Supply) / (Initial Supply)] * Initial Price * Virality Score

• Sell Price = Lesser of [Buy Price] or [(Percent Allocation) * (Sum of Total Price of Nibs Purchased)]

• Percent Allocation = (Weight At Supply N) / (Total Weight Of All Nibs Outstanding)