Pluto is an innovative reserve currency design. It is a financial instrument resistant to bear markets that provides long-term and planned growth in the market price of an asset.

The main metric of the protocol is the growth of the collateral value of each PLUTO token.

The collateral is implemented by the Treasury, where parameters are controlled by voting, and can also change automatically depending on market figures. The mathematical model of Pluto is mostly focused on Treasury growth. It is built with this objective in mind.

The Treasury growth is driven by the funds of PLUTO users. The users can define that growth by means of PLUTO release mechanism. The mechanism implies that the Treasury is spent only in case the PLUTO token price falls below the backed price. This approach ensures that the market price never settles below the backed price.

At least 80% of the Treasury is comprised of stablecoins. The stablecoins are used for liquidity mining in money markets such as https://vires.finance. The Treasury also includes liquidity provider tokens in the parent pool of PLUTO, a megapool launched on the Puzzle Swap service.

The list of supported assets can be expanded by voting conducted by stakers. Still, their share in the Treasury must never exceed 20% to ensure that the liquidity providing remains stable.

The PLUTO model is based on several key mathematical parameters that ensure the stability of the system and PLUTO’s rate as well. Those parameters are namely: Backed Price (Min Price), Market Price and Max price.

Definitions: Total Supply – the number of PLUTOs issued Treasury Value – an equivalent of assets in the Treasury in USDN

Hence: Backed Price (Min Price) = Treasury Value / Total Supply. Market Price = PLUTO price to USDN on the market. Max Price = Backed Price * K, where K is a number set by voting, the default value is 3. Pluto Growth Factor = Market Price / Backed Price.

Pluto Growth Factor demonstrates the correlation of PLUTO’s market price with the real secured price. Theoretically, Pluto Growth Factor has limited boundaries, it should not go beyond the range: [100%, 100%*K]. The optimum size of Growth Factor is considered the central point of this range, i.e. 200%.

The price of PLUTO never goes instantly too high while balancing between Backed Price and Max Price. PLUTO is designed as a reserve currency, so this approach ensures a stable growth rate in the long term. PLUTO is guaranteed not to fall in price by more than (K-1)/K.

Importantly, the Backed Price is practically a non-decreasing value. In a stable peg of stablecoins, the downside risk of the Backed Price is 20%, provided all non-stablecoins in the coffers drop in price to 0.

Suppose the Treasury consists of 1 million USDN yields on Vires, also 500K PLUTOs are issued. This means that the Backed Price of PLUTO = 1000 / 500 = 2 USDN.

On the market PLUTO is traded at 4 USDN, so Pluto Growth Factor = 100 * 4 / 2 = 200%. Hence, 200% is a basic figure, at which staking brings regular returns, and the onboarding bonus is most attractive for new users.

The market price may however fluctuate. As an example, the PLUTO price can exceed 6 USDN, thus going over the Max Price. In this case, new PLUTO tokens will be issued by the protocol. The new tokens are then sold for USDN and the USDNs will be added to the Treasury, thus increasing its size.

Alternatively, if the market price of PLUTO falls below the Backed Price, the Treasury funds will serve for PLUTO buyback to secure its price from going even lower.

Thus, too sharp fluctuations of the market exchange rate make the benefit of the Treasury. This approach guarantees the system’s stability and keeps its behavior predictable enough, making PLUTO a reliable reserve currency.

When purchasing PLUTO, the user can count on the fact that its market price will not fall below the Backed Price apart from certain exotic phenomena such as bank runs or depreciation of stablecoins.

The basic mechanism of issuing PLUTO tokens is onboarding. A user can exchange one of the supported LP-tokens for Pluto at the market price and receive an Onboarding Bonus.

The Onboarding Bonus has an impressive size. The user receives PLUTO tokens instantly at the market rate. These tokens may be unlocked after a lock-up period with onboarding APY bonuses credited in PLUTO.

The lock-up period and the size of the APY depend on the Growth Factor at the time of release:

The specified APY accrues on the number of PLUTOs the user has issued, during the lockup days. At the end of the lockup period, the PLUTOs are automatically converted to regular staking and continue returning a stable interest.

The lockup duration as well as the onboarding bonus can be changed depending on the market conditions and through voting. If the Growth Factor is below 110%, i.e. if Market Price < Backed Price * 1.1 onboarding is impossible and users can only buy the token from the market, while its price is favorable enough.

A Project Development Fund will be established by the Dev Team to sponsor further improvement of PLUTO reserve currency. It’s important that every PLUTO token that the Fund receives should be backed. Therefore, an extra of 0.24% to 1.72% of all PLUTOs paid to onboarding participants will be minted for that purpose. This fee will be sent to the team’s wallet and will be automatically staked.

In order to stimulate the coin's growth at low PLUTO Growth Factor values, buying pressure is implemented through Automatic Buyback mechanism.

A portion of the onboarding funds serves to buy back PLUTOs from the megapool on Puzzle Swap. The portion that is allocated to the buyback instead of being added to the Treasury is determined by the Buyback Ratio variable and is also subject to change depending on market sentiment and voting.

The dependence table indicates that the closer PLUTO falls to its "floor", i.e. to the Backed Price value, the more funds are allocated for the Buyback to ensure the price is pushed away from the "floor".

Importantly, the Buyback does not trigger the Backed Price fall. The Buyback Ratio is adjusted as to buy back as much as possible at Growth Factor values of 110-130%.

Suppose the market price of PLUTO is 5 USDN and backed price = 3 USDN. This means the Growth Factor equals 166%. A User brings 10000 USDN for PLUTO minting by onboarding. 4440 USDN will then be used for instant Buyback while the remaining 5560 USDN will be passed to the Treasury.

The User will receive appr. (10000 / 5.02) 1992 PLUTOs, that considering the price impact resulted by the Buyback. These 1992 PLUTOs will automatically go to onboarding for 9 days at 1798% APY. Thus, the User will be able to redeem (1992 * 1.0752) 2141,9 PLUTOs at the end of the lock-up period.

In order to implement the governance function and to encourage PLUTO holders, staking without locking-up principle is to be implemented. That means that PLUTO staking or unstaking are both permitted at any time.

The staking reward will consist of two parts: Unconditional Reward and an additional Incentive Staking Reward.

The Unconditional APY is equal to the protocol's Treasury APY. The Incentive APY is determined based on the Growth Rate of the Treasury and the limit indicated by the user vote:

Incentive Staking Reward = min(max(Incentive Staking Rate, Voted Incentive)), so max Incentive Staking Rate is:

Suppose there is an equivalent of 100 million USDN in the Treasury, generating an annual income of 20%, which equals 20 million a year. All users have staked 10 million PLUTOs out of a total existing 20 million.

The collateral grows by 20% per year at the expense of the Treasury APY. With only half of the available PLUTOs staked, this allows for an unconditional staking yield of 20% * 2 = 40%.

Also, there is an incentive emission. Suppose it has been determined by voting to be 60%. Again, depending on the staked PLUTOs share, the real incentive APY is 120%.

In such a scenario, the total PLUTO staking yield will be 40 + 120 = 160% p.a. without a lock-up. This yield is measured in PLUTOs notwithstanding its Backed Price growth, i.e. actual capital growth over the year is assumed to be higher than the APY.

The key objective of the protocol is to increase the collateral value of each PLUTO (i.e. Backed Price) which boosts an increase of the max Price and the equilibrium Market Price.

For this, the protocol must ensure that while staking and onboarding the generated share of the Treasury value growth should always exceed the fraction by which PLUTO's overall supply increases per unit of time. That means, mathematically, the PLUTO Growth Rule is:

If we break down the growth of the Treasury and the growth of coin minting into components, we should get the following:

Consequently, to ensure growth the Protocol should conduct onboarding in such a way that the amount of Treasury’s onboarding fraction might grow faster than the amount of aggregate output from PLUTO in the form of accumulated onboarding interest, in order to provide room to pay for incentive staking.

This is accomplished due to the fact that onboarding is done at Market Price*(1-premium), while the cost of Treasury per token is equal to Backed Price. Therefore, the Protocol always sticks to the rule that Backed Price <= Market Price*(1-premium).

The Backed Price Growth depends on the aggregate Onboarding, Staking, Treasury APY, and Bonding Buyback parameters. It is calculated as:

While based on a model implementing a systematic increase of the Backed Price, PLUTO becomes a coin with persistent growth embedded in its principle. Thus, PLUTO is a bearish season resistant reserve currency that creates an incentive for liquidity growth in the ecosystem.

Pluto is an innovative reserve currency design. It is a financial instrument resistant to bear markets that provides long-term and planned growth in the market price of an asset.

The main metric of the protocol is the growth of the collateral value of each PLUTO token.

The collateral is implemented by the Treasury, where parameters are controlled by voting, and can also change automatically depending on market figures. The mathematical model of Pluto is mostly focused on Treasury growth. It is built with this objective in mind.

The Treasury growth is driven by the funds of PLUTO users. The users can define that growth by means of PLUTO release mechanism. The mechanism implies that the Treasury is spent only in case the PLUTO token price falls below the backed price. This approach ensures that the market price never settles below the backed price.

At least 80% of the Treasury is comprised of stablecoins. The stablecoins are used for liquidity mining in money markets such as https://vires.finance. The Treasury also includes liquidity provider tokens in the parent pool of PLUTO, a megapool launched on the Puzzle Swap service.

The list of supported assets can be expanded by voting conducted by stakers. Still, their share in the Treasury must never exceed 20% to ensure that the liquidity providing remains stable.

The PLUTO model is based on several key mathematical parameters that ensure the stability of the system and PLUTO’s rate as well. Those parameters are namely: Backed Price (Min Price), Market Price and Max price.

Definitions: Total Supply – the number of PLUTOs issued Treasury Value – an equivalent of assets in the Treasury in USDN

Hence: Backed Price (Min Price) = Treasury Value / Total Supply. Market Price = PLUTO price to USDN on the market. Max Price = Backed Price * K, where K is a number set by voting, the default value is 3. Pluto Growth Factor = Market Price / Backed Price.

Pluto Growth Factor demonstrates the correlation of PLUTO’s market price with the real secured price. Theoretically, Pluto Growth Factor has limited boundaries, it should not go beyond the range: [100%, 100%*K]. The optimum size of Growth Factor is considered the central point of this range, i.e. 200%.

The price of PLUTO never goes instantly too high while balancing between Backed Price and Max Price. PLUTO is designed as a reserve currency, so this approach ensures a stable growth rate in the long term. PLUTO is guaranteed not to fall in price by more than (K-1)/K.

Importantly, the Backed Price is practically a non-decreasing value. In a stable peg of stablecoins, the downside risk of the Backed Price is 20%, provided all non-stablecoins in the coffers drop in price to 0.

Suppose the Treasury consists of 1 million USDN yields on Vires, also 500K PLUTOs are issued. This means that the Backed Price of PLUTO = 1000 / 500 = 2 USDN.

On the market PLUTO is traded at 4 USDN, so Pluto Growth Factor = 100 * 4 / 2 = 200%. Hence, 200% is a basic figure, at which staking brings regular returns, and the onboarding bonus is most attractive for new users.

The market price may however fluctuate. As an example, the PLUTO price can exceed 6 USDN, thus going over the Max Price. In this case, new PLUTO tokens will be issued by the protocol. The new tokens are then sold for USDN and the USDNs will be added to the Treasury, thus increasing its size.

Alternatively, if the market price of PLUTO falls below the Backed Price, the Treasury funds will serve for PLUTO buyback to secure its price from going even lower.

Thus, too sharp fluctuations of the market exchange rate make the benefit of the Treasury. This approach guarantees the system’s stability and keeps its behavior predictable enough, making PLUTO a reliable reserve currency.

When purchasing PLUTO, the user can count on the fact that its market price will not fall below the Backed Price apart from certain exotic phenomena such as bank runs or depreciation of stablecoins.

The basic mechanism of issuing PLUTO tokens is onboarding. A user can exchange one of the supported LP-tokens for Pluto at the market price and receive an Onboarding Bonus.

The Onboarding Bonus has an impressive size. The user receives PLUTO tokens instantly at the market rate. These tokens may be unlocked after a lock-up period with onboarding APY bonuses credited in PLUTO.

The lock-up period and the size of the APY depend on the Growth Factor at the time of release:

The specified APY accrues on the number of PLUTOs the user has issued, during the lockup days. At the end of the lockup period, the PLUTOs are automatically converted to regular staking and continue returning a stable interest.

The lockup duration as well as the onboarding bonus can be changed depending on the market conditions and through voting. If the Growth Factor is below 110%, i.e. if Market Price < Backed Price * 1.1 onboarding is impossible and users can only buy the token from the market, while its price is favorable enough.

A Project Development Fund will be established by the Dev Team to sponsor further improvement of PLUTO reserve currency. It’s important that every PLUTO token that the Fund receives should be backed. Therefore, an extra of 0.24% to 1.72% of all PLUTOs paid to onboarding participants will be minted for that purpose. This fee will be sent to the team’s wallet and will be automatically staked.

In order to stimulate the coin's growth at low PLUTO Growth Factor values, buying pressure is implemented through Automatic Buyback mechanism.

A portion of the onboarding funds serves to buy back PLUTOs from the megapool on Puzzle Swap. The portion that is allocated to the buyback instead of being added to the Treasury is determined by the Buyback Ratio variable and is also subject to change depending on market sentiment and voting.

The dependence table indicates that the closer PLUTO falls to its "floor", i.e. to the Backed Price value, the more funds are allocated for the Buyback to ensure the price is pushed away from the "floor".

Importantly, the Buyback does not trigger the Backed Price fall. The Buyback Ratio is adjusted as to buy back as much as possible at Growth Factor values of 110-130%.

Suppose the market price of PLUTO is 5 USDN and backed price = 3 USDN. This means the Growth Factor equals 166%. A User brings 10000 USDN for PLUTO minting by onboarding. 4440 USDN will then be used for instant Buyback while the remaining 5560 USDN will be passed to the Treasury.

The User will receive appr. (10000 / 5.02) 1992 PLUTOs, that considering the price impact resulted by the Buyback. These 1992 PLUTOs will automatically go to onboarding for 9 days at 1798% APY. Thus, the User will be able to redeem (1992 * 1.0752) 2141,9 PLUTOs at the end of the lock-up period.

In order to implement the governance function and to encourage PLUTO holders, staking without locking-up principle is to be implemented. That means that PLUTO staking or unstaking are both permitted at any time.

The staking reward will consist of two parts: Unconditional Reward and an additional Incentive Staking Reward.

The Unconditional APY is equal to the protocol's Treasury APY. The Incentive APY is determined based on the Growth Rate of the Treasury and the limit indicated by the user vote:

Incentive Staking Reward = min(max(Incentive Staking Rate, Voted Incentive)), so max Incentive Staking Rate is:

Suppose there is an equivalent of 100 million USDN in the Treasury, generating an annual income of 20%, which equals 20 million a year. All users have staked 10 million PLUTOs out of a total existing 20 million.

The collateral grows by 20% per year at the expense of the Treasury APY. With only half of the available PLUTOs staked, this allows for an unconditional staking yield of 20% * 2 = 40%.

Also, there is an incentive emission. Suppose it has been determined by voting to be 60%. Again, depending on the staked PLUTOs share, the real incentive APY is 120%.

In such a scenario, the total PLUTO staking yield will be 40 + 120 = 160% p.a. without a lock-up. This yield is measured in PLUTOs notwithstanding its Backed Price growth, i.e. actual capital growth over the year is assumed to be higher than the APY.

The key objective of the protocol is to increase the collateral value of each PLUTO (i.e. Backed Price) which boosts an increase of the max Price and the equilibrium Market Price.

For this, the protocol must ensure that while staking and onboarding the generated share of the Treasury value growth should always exceed the fraction by which PLUTO's overall supply increases per unit of time. That means, mathematically, the PLUTO Growth Rule is:

If we break down the growth of the Treasury and the growth of coin minting into components, we should get the following:

Consequently, to ensure growth the Protocol should conduct onboarding in such a way that the amount of Treasury’s onboarding fraction might grow faster than the amount of aggregate output from PLUTO in the form of accumulated onboarding interest, in order to provide room to pay for incentive staking.

This is accomplished due to the fact that onboarding is done at Market Price*(1-premium), while the cost of Treasury per token is equal to Backed Price. Therefore, the Protocol always sticks to the rule that Backed Price <= Market Price*(1-premium).

The Backed Price Growth depends on the aggregate Onboarding, Staking, Treasury APY, and Bonding Buyback parameters. It is calculated as:

While based on a model implementing a systematic increase of the Backed Price, PLUTO becomes a coin with persistent growth embedded in its principle. Thus, PLUTO is a bearish season resistant reserve currency that creates an incentive for liquidity growth in the ecosystem.