Klima 2.0

The Dark Sole Enterprise Ltd
ds@darksole.vip

With contributions from scott@klimadao.finance

April 16, 2025

An Autonomous Asset Manager incorporating Asset pricing, Liquidity and Bond Markets powered by a Dual Token structure designed for efficient and rational decentralised liquidity within the carbon credit asset class.

Version 1.43

1 Prologue

Klima 2.0 constitutes an autonomous capital system for the Carbon asset class. It is neither a conventional token nor a traditional protocol, but rather a continuously adaptive financial structure governed entirely by endogenous signals and risk-weighted economic inputs.

The system is based on a dual-token architecture: KLIMA, representing capital and asset exposure, and KlimaX, reflecting systemic risk preferences. Together, these tokens structure the internal market dynamics without the need for oracles or discretionary oversight. This architecture enables the system to:

• Systematically select and price tokenised Carbon credits,

• Construct and maintain a forward-yield curve derived from on-chain capital commitments,

• Govern portfolio allocation, liquidity provisioning, and incentive distribution through deterministic smart contract logic.

All token-holder actions – staking, selection, and locking – serve as inputs to a reflexive coordination mechanism. KLIMA governs the allocation of capital to carbon assets, while KlimaX parametrises the system’s risk assumptions and pricing capacity. This interaction defines a synthetic balance sheet where capital value, risk spread, and yield formation emerge from collective participation.

The platform consists of three interdependent components: the Portfolio Manager, which acquires and retires Carbon assets; the Bond Market, which generates a time-structured synthetic yield curve; and the Liquidity Market, which facilitates price discovery and capital flow across KLIMA, KlimaX, and external currencies. These mechanisms are interlocked by design, enabling the system to continuously seek equilibrium.

Klima 2.0 abstracts complex market operations into a formal economic structure that integrates asset management, governance, and liquidity within a single protocol. KLIMA offers structured exposure to carbon markets through tokenised yield and asset ownership, while KlimaX modulates this exposure in response to endogenous risk metrics.

In this model, staking constitutes an economic vote; liquidity provision informs portfolio capacity; and yield is an emergent function of structural configuration. The system is designed to operate without exogenous intervention, maintaining equilibrium through adaptive incentive distribution and real asset correlation.

Klima 2.0 is a closed-form capital system with embedded governance and economic reflexivity, capable of continuously modelling and adjusting its internal state through its own token dynamics.

2 Klima 2.0

KlimaDAO was originally launched to create market infrastructure driving seamless liquidity for Carbon monetisation and Carbon retirement. It has been constructed using decentralised architecture with a token system ‘KLIMA’ for dynamic economic governance. Whilst it has been successful in brand and customer acquisition, as well as ownership of real Carbon assets, the current token model and processes are unwieldy and will not allow the product to scale to its potential given the opportunity of this market.

Hence we present Klima 2.0 as an Autonomous Asset Manager (AAM) with the new Risk-Balanced Asset (RBA) token KLIMA that:

• Selects and purchases Carbon credits on a spot and forward basis for its own Portfolio.

• Retires its credits by issuing Offset certificates to buyers.

• Continuously Yields Carbon from its Portfolio.

• Enables investors to:

  • Hold a true passive exposure to Carbon markets, spreads and dislocations via the new KLIMA token.

  • Actively reflect their risk appetite collectively to optimise Portfolio selection and capacity.

  • Determine the proportion of Yield distribution vs capital retention allowing cyclical expansions and contractions and de facto price modelling of the KLIMA token.

Klima 2.0 provides a fundamental capital, liquidity and execution layer for wholesale Carbon trading, capturing spreads and structural pricing across the asset class. It employs rational adaptive financial models to reflect token-holders’ collective risk-reward preferences, produced solely through native smart contract balances from staking and liquidity functions allowing price discovery and harmonious functions to govern the stability and risk of the RBA token KLIMA.

The RBA model grants clean look-through economic ownership of tokenised Carbon assets to KLIMA token-holders, as well as self-governance for risk and reward allowing maximum flexibility in this hybrid capital instrument for growth and distribution.

2.1 Dual Utility tokens

In addition to the KLIMA token, Klima 2.0 introduces a second Risk Governance token KlimaX. This token is responsible for modelling risk across the ecosystem by responding to the KLIMA token’s core selections and adding essential derivative parameters that manage adverse selection and pricing capacity.

KLIMA tokens have the beneficial ownership of the Portfolio and set core allocation choices, whereas KlimaX acts as the risk-seeking gauge for the portfolio construction.

KlimaX is formally compensated with KLIMA tokens hence the two tokens’ interests are fully aligned and together perform dynamic Portfolio optimisation as a result of collective owner utility-function.

2.2 High level Architecture

Three economic pillars support the Klima 2.0 AAM:

1. Portfolio Manager:

   • Accumulates Carbon credits for the Portfolio by minting KLIMA.
   • Sells Carbon Offset certificates from the Portfolio by buring KLIMA.
   • Prices Spot and Forward delivery Carbon using the system generated curve.

2. Bond Market:

   • KLIMA holders Stake irreversibly for a fixed time period.
   • Those Staking are able to select Carbon assets for the Portfolio.
   • The Staking pattern over time creates a KLIMA Yield curve, which is distributed to Bond-holders. This is utilised for Forward delivery pricing in the Portfolio Manager and weightings for Bond-holders in governance and for their Spot Carbon Yield distribution.

3. Liquidity Market:

   • KLIMA and KlimaX holders are able to pair their tokens together, or in the case of KLIMA with USDC, in order to generate liquidity fees.
   • Locking Liquidity (Staking LP tokens) generates a share of the KLIMA Yield.
   • Locked KLIMA:KlimaX liquidity participates in general governance alongside Bond-holders.

Noting that Staking and Locking are used interchangeably throughout the paper and for this model are identical functions where asset-transfers are disabled for the period specified.

2.3 Economics and Incentives

2.3.1 KLIMA Synthetic Yield

KLIMA emits a continuous Yield rewarding:

1. KLIMA Bond-holders.

2. KlimaX Staking.

3. Both KLIMA and KlimaX Liquidity Provders (LPs).

The proportions and quantities are dynamic depending on the system state.

2.3.2 KlimaX Incentives

The expansion of the KlimaX token supply is allocated to stakeholders below in varying quantities depending on system balances.

1. KLIMA Bond-holders.

2. KlimaX Staking.

3. Both KLIMA and KlimaX Liquidity Provders (LPs).

2.3.3 Carbon Yield

Assuming the Portfolio holds spot Carbon credits, the Portfolio Manager emits a continuous Carbon Yield to KLIMA Bond-holders only with the proportion a function of the system state.

2.4 Portfolio Manager

At the core of the platform, the Portfolio Manager accumulates, trades and distributes its Carbon Portfolio driven by parameters determined from collective token-holder actions (and inaction).

The AAM purchases Carbon credits and sells Offset certificates by pre-defined classification (‘Class’). It does not sell Carbon credits as those are issued through the Portfolio Yield function.

Token-holders collectively set the risk parameters for pricing of each Class by defining:

• Portfolio weighting.

• Capacity curve and spreads.

Additional global parameters are similarly determined:

• Forward-delivery discount rates.

• Synthetic yield curve creating incentives for Portfolio selection, liquidity provision and risk management contributions.

• Proportion of Liquid Carbon credit yield released for KLIMA to token-holders.

There are no oracles or external inputs required for Klima 2.0 as it is fully autonomous and responds to its own native state of token balances.

2.5 Tokens

2.5.1 Carbon Registry

Holders of physical Carbon credits can create tokenised representation of their assets through the Registry function. Here, physical assets are swapped for their respective C tokens, based on the Registry’s classification system and the delivery schedule.

Once C tokens are created they can be sold to the AAM, or retired back at the Registry to create the offset certificates (denoted C*).

2.5.2 Risk Balanced Asset Token: KLIMA

KLIMA represents core ownership of the Portfolio assets, and is designed to flex between asset and growth value drivers depending on token-holder activity.

KLIMA has no maximum supply but inflates upon Carbon credit accumulation, and contracts upon issuance of Offset certificates.

• When Locked for fixed maturities:

  • Option to select Carbon classes for Portfolio weighting and pricing (‘Active’).

  • Sets the Forward discount rate for Carbon Portfolio acquisition from collective Staking pattern over time.

  • Generates a Synthetic yield of KLIMA based on Forward curve and a real Carbon yield based on Active selection ratio.

  • Participates in governance for whitelisting Carbon assets.

• Transactional usage:

  • Mint: New KLIMA issued by the Portfolio Manager to purchase new Carbon credits for the Portfolio.

  • Burn: KLIMA are Purchased by the Portfolio Manager to issue Offset certificates.

• Locked Liquidity:

  • Generates a time-based relative share of the KLIMA Synthetic Yield, reflecting the risks taken to support the price of platform capital.

Noting that the tokens can delegate utility as required.

2.5.3 Risk Governance Token: KlimaX

KlimaX is a fixed-supply token issued programmatically over time with a dynamic allocation for Incentives.

• When Locked:

  • Shapes the pricing curve and spread of KLIMA.
  • Determines risk premia for LPs.
  • Generates a share of Synthetic Yield.
  • Receives KlimaX Incentives.

• Locked Liquidity:

  • Generates a share of Synthetic Yield.
  • Participates in governance.
  • Receives KlimaX incentives.

2.5.4 Staking functions

The A token has 2 staking functions which are not independent:

1. Bonds: The KLIMA token is locked for a specific period of time representing a liquidity preference for the holder in return for Yield. This part of the stake cannot be amended.

2. Price: Collective selection of Carbon classes by KLIMA staking determines the instantaneous price ratio for KLIMA token issuance. This selection can be amended and withdrawn at any time to allow price modulation for the platform of its Carbon assets.

The KlimaX token has a single staking function that also optionally selects Carbon classes. This determines the rate of issuance or price curve of KLIMA for the specified Carbon, as well as the retirement burning rate.

Both tokens facilitate the Klima Carbon market to function efficiently with the KLIMA token responsible for Portfolio selection and pricing, and the KlimaX token modulating capacity and risk.

2.6 Initialisation of the KLIMA Token

The Klima Protocol has approximately 20 million tonnes of Carbon credits in its Treasury as assets, which will be used to create the initial issuance of KLIMA tokens upon launch of Klima 2.0.

2.7 End Users

1. Carbon Credit Sellers

   Those wishing to monetise spot or forward delivery classes of Carbon.

   Portfolio Manager: Continuously acquires C tokens using an autonomous pricing strategy, based on class, delivery and token balances, issuing new KLIMA tokens as consideration to build the C Portfolio.

2. Offset Buyers

   Those wishing to obtain the offset certificate by retiring Carbon credits from the Portfolio.

   Portfolio Manager: Continuously sells offset certificates, by Burning KLIMA tokens and issuing the Offset certificate C*, by retiring the C token quantity in the Registry.

3. Investors

   Those who wish to own a liquid, or yielding locked fixed-maturity financial exposure, to a basket of Carbon assets.

   Bond Market: Provides a daily time-based yield on for those Staking KLIMA tokens, comprised of both a synthetic and real Portfolio carbon C component.

4. Liquidity Providers

   Those who wish to generate liquidity fees on their portfolio of Klima 2.0 Assets coupled together or with USDC.

   Liquidity Market: LPs are incentivised by the Synthetic Yield calculated from system metrics to compensate them for risk.

5. Active Portfolio Optimisation

   KlimaX and KLIMA Asset Selection: The Staking Incentives and allocations are designed for those who wish to participate in overall risk management to collectively resolve for the optimal Portfolio risks.

2.8 AAM Highlights

• Decentralised Architecture:

  The AAM is smart contract based, fully autonomous as to pricing and distribution of its assets with governance power held by risk-based capital.

• Adverse Selection:

  The AAM does not permit the direct purchase of Carbon credit C tokens from its Portfolio (Offsets only), but rather yields C tokens on a Portfolio basis over time.

• C Tokens:

  Users with C tokens can always access offset certificates through the Registry, hold the specific C token or sell back to the AAM if required. Secondary markets and utility for C tokens may emerge over time.

• Implied Spreads:

  The AAM purchases C tokens at relative discounts based on capacity pricing and forward discount curves folding natural returns into the Portfolio capital.

• Dual Tokens:

  Whilst the KLIMA token reflects asset economics, the KlimaX token is essential for optimising pricing capacity in return maximising risk-adjusted spreads for the Portfolio. Since its earnings power is a function of the KLIMA token value, its role as this spread optimiser is truly economically aligned and as such fundamental values of KLIMA and KlimaX are highly correlated.

• Hybrid Asset Model

  The rate of C token yield for KLIMA generated from the underlying Portfolio is derived from the system state of the KLIMA token balances.

  • This enables investors collectively to model capital and yield proportions, allowing the price of the capital token to discover its equilibrium value with respect to the combination of current and projected underlying Portfolio value.

  • This flexibility enables a ‘Pull to par’ effect as growth expectations lower, whilst not limiting price appreciation potential in high growth projection markets.

  • The hybrid model incorporates both asset stabilisation plus equity-like returns.

  Critically this approach enables the KLIMA token to act as a true medium of exchange for the Carbon trading activity of the users, propagating the feedback loops to both the KLIMA and KlimaX tokens.

3 Core Economic Pillars

In this Section we refer to KLIMA and KlimaX tokens as A and G respectively.

The three tenets of Klima 2.0 enable the model to find equilibrium through continuous dynamic feedback loops and system balances. There is no oversight or centralised management entity with discretionary powers.

1. Bond Market: A token holders stake tokens until a set expiry to create floating yield Bonds and have the ability to select Carbon Classes for Portfolio weighting.

   • The collective temporal staking pattern produces a Synthetic Yield curve in A tokens to reward Bond-holders, as well as price the forward curve for the AAM.

   • A real yield of spot-delivery C tokens is issued continuously from the Portfolio to Bond-holders depending on the participation in Portfolio weightings.

   • Only A tokens participate in the Bond Market.

2. Portfolio Manager: The Portfolio Manager swaps its own token A for Carbon C (in) or Carbon offset certificates C* (out) to build a Portfolio of Carbon credits.

   • Both Locked A and G are used in the Portfolio Manager whereby A Staking determines the pricing of any given Carbon class, and G determines the rate of acquisition (disposal).

     Only Bond-holders (Time-locked A) can participate in Portfolio weighting although it is not mandatory.

   • Forward-delivery Carbon (for a set of fixed dates out to 10 years) is transacted simultaneously with spot liquid Carbon.

3. Liquidity Market: Here the tokens are traded in 2 core liquidity pairs with various incentives available to Liquidity Provider token holders (LPs), including a Risky Yield generated by the Bond Market Synthetic Yield.

   • AG: Native token swap A and G.

   • AQ: The asset token A with USDC Q.

   The Liquidity Market provides the complementary facility to the Bond Market and the critical relationship between the native tokens and the hard currency of USDC.

The Klima 2.0 system enables each participant in the various economic pillars to act in the interests of their own capital and utility, which through the harmonic model, enables price discovery, liquidity and stability for Carbon trading which creates positive reinforcement cycles as catalysts for growth and scale.

3.1 Bond Market

Holders of A can Stake (select) a Bond maturity from the set of Standard maturities. Bonds expire every 90 days on a rolling basis. There are always 40 maturities extending out to approximately 10 years for Bond staking.

• Forward Curve: Aggregate Bond-staking determines the shape of the discount curve of the A token with regards to its purchasing rate of forward-delivery Carbon.

• Synthetic Yield: Bond-holders receive a floating yield of new A tokens on their stake following the shape of this discount curve. Yield is calculated daily and accumulates to the principal stake.

• Real Carbon Yield: Liquid Carbon in C token form is emitted to Bond-holders on a daily basis assuming the portfolio holds spot Carbon assets. The emission rate responds to Bond-holders staking for Portfolio pricing and up to ~22% per quarter is released.

• Liquidity: There is no early unlocking; all principal and accumulated yield is released only at Bond maturity.

G Tokens are not involved in the Bond market. The forward curve is agnostic to Carbon class although only Bond-holders can select Carbon classes for Portfolio pricing.

3.1.1 Synthetic Yield and Forward-Delivery Curve

Defining:

• : Total A tokens staked for Bonds expressed as a proportion of outstanding supply of A.

• : Total A tokens staked for Bond maturity bucket , expressed as a proportion of outstanding supply of A, where , and  is the index of standard maturities .

• : Time to expiry expressed in years.

Calculating curve parameters , :

The shape of the yield curve is produced:

Normalising  to :

With the cumulative sum of the normalised values expressed as :

The zero coupon yield curve  is solved:

Whereupon, the Bond discount rate  that forms the Forward delivery curve is derived:

The yield due on A Bonds is calculated daily and added to staked principal, hence the daily yield for each time bucket is calculated as :

Hence, any bond stake  will increase by :

With the total A tokens created on a daily basis for Bond inflation as :

For visualising the sensitivity of A overall inflation rates with respect to staking and duration, Figure 8 assumes a single maturity over the staking range to provide an approximation of inflation .

3.1.2 Governance Weightings

Governance rights, for example the whitelisting (blacklisting) of Carbon classes, and any other matter requiring token stakeholder voting, are allocated to two cohorts:

1. Bond staking:

2. Locked liquidity in the A-G pair AG (see Section 3.3) defined here as , representing the quantity of A tokens held in the liquidity pool expressed as a proportion of circulating supply.

Voting power is allocated by time and applied to the respective balance of A:

1. Initial voting weights for Bonds :

2. Initial voting weights for LPs :

3. Final voting weights Bonds :

4. Final voting weights LPs :

3.1.3 Real Carbon Yield

Defining:

• : Total A tokens Staked for pricing of Carbon classes, expressed as a proportion of outstanding supply of A Tokens.

With  as the daily emission factor applied to the Portfolio holding spot delivery C tokens:

Carbon Yield is allocated to Bond-holders using (normalising) the initial voting weight  determined in Equation (11).

3.2 Portfolio Manager

The Portfolio Manager role of swapping A for Carbon is managed through a set of smart contracts driven by Staking choices from the token system, the balances of assets held, and the discount curves generated by the Bond market.

The combined staking of A and G Tokens creates a dynamic pricing matrix by class of Carbon and by time, enabling spot and forward trading of Carbon.

3.2.1 Purchase Carbon

Users swap C for A

Existing Carbon in the Portfolio

Carbon classes  are whitelisted through governance by the A token and the AG LP holders (see Section 3.1.2).

For Carbon pricing, both the A tokens and the G tokens may stake for specific Carbon classes  and these are independent stakes between the two token systems.

For a Carbon class quantity to be sold to the AAM, it must have a strictly positive quantity of A tokens staked for that Carbon class, otherwise there is no price, and the Carbon cannot be sold.

Defining:

• : Total tonnes of Carbon class  currently held in the Portfolio.

• : A tokens staked for Carbon class  expressed as a proportion of outstanding supply of A Tokens where .

• : G tokens staked for class  expressed as a proportion of outstanding supply of G Tokens.

• : The quantity of Carbon class  held in the AAM deliverable per maturity  where  reflects the liquid quantity.

In order to determine the present-value quantity of Carbon, , we apply the discount curve from Equation (7) to the liquidity schedule and sum the discounted holdings:

Similarly, taking  as the quantity of Carbon  to be sold with a specific maturity index :

Once standardised by the discount curve, trades can be aggregated in the same class for the defined trade or auction period.

Where  is expressed as the relative increment to its respective pool balance, the amount of A tokens issued to pay for Carbon, , expressed as a proportion of current supply, is determined as:

Denoting the expression on the right hand side of Equation (18) as :

Finally, is applied to the outstanding supply of A to solve for token quantities.

Figure 11 illustrates the G token capacity to maintain the initial Portfolio pricing of the A token. The data has been normalised in Figure 12 to .

Noting that the sensitivity to  increases as  increases and the effects become more pronounced as  increases.

Zero Carbon Scenario

There are circumstances when there is zero Carbon held in the Portfolio for a particular class, i.e. , which invalidates the calculation of  and a different approach is required.

Taking  as the tonnes of Carbon tokens (implying an existing balance of 1 tonne), adjusted for forward discounting, to be sold for any Carbon class that has a strictly positive A stake , together with G stake :

3.2.2 Sell Offset Certificates

Users swap A for C*

Weighted Carbon Class

For retiring Carbon that is weighted, that is there is a strictly positive A token stake for that class, an A token holder can extract the Carbon class offset of their choice  but the available pool is only the liquid balance, namely the element :

As before denoting the expression on the right hand side of Equation (21) as :

Figure 15 shows the cost of Carbon increasing with  and decreasing on .

Unweighted Carbon Class

An offset for Carbon class with a zero A stake cannot be extracted from the portfolio by swapping in A tokens. However, it is part of the Portfolio yield detailed in Section 3.1.3.

Liquidation:

In the event that 100% of A tokens are placed into the burn mechanism for Carbon Offsets, the balances of all Carbon held in the Portfolio post-trade are distributed to all G holders.

Figure 16 below shows the spread captured on a ‘Round trip’ by the system where  is the proportion retained:

Figure 17 shows the component `Spread’ contributions on a Carbon sale and purchase of offset round trip.

3.3 Liquidity Markets

Both A and G tokens can be used independently of price (and time) staking for providing liquidity.

There are two core liquidity pools:

1. An AAM 50:50 pairing of A and G tokens; pool AG.

2. A hard currency USDC denoted as Q paired with A; pool AQ.

3.3.1 Liquidity Fees

The AQ pool will have its own set of fees in the normal way.^[1]

The AG pool has different economics as the assets are highly correlated since they represent the same economy. For this reason, the fees are extremely low.

By locking liquidity (LP tokens) to the standard maturities, both pools may receive a distribution of A tokens determined from the Risky Yield calculation below. This is an additional primary issuance to the Bond Synthetic Yields already discussed.

3.3.2 Risky Yield: Beta Determination

We can consider the Bond market yield as the system risk-free rate. In addition to this mechanism, a risky spread is determined that is ultimately paid to the liquidity providers of the A and G tokens as compensation for the risk levels assumed.

As we have seen, the G token has an impact on risk-pricing of A. As G staking increases, the relationship between the Carbon class selected under  and the Portfolio token A strengthens. We can consider  staking as an estimate of residual or idiosyncratic risk in the carbon-class and this allows us to calculate a Portfolio beta  from the implied betas of each carbon class .

The Portfolio  determines a yield factor for the liquidity pools of A to compensate for the implied risk levels.

For intuition, the map in Figure 19 shows the various outputs of the function per Class.

The table and figure below show an example of the effects on  on allocating large  values to small  values where the shift in  results in a lower  (0.27 from 0.55) with no change to total G and A staking.

Figure 20 shows the  sensitivity to G staking as a function of A stake; that is to say that a large  stake on a small  stake has limited effects (notwithstanding other consequential factors).

3.3.3 Allocation of Risk Premium

The full issuance of A tokens is depicted below including now the risky premium for the liquidity pools accordingly.

3.3.4 Share of Risky Premium

The risky premium allocation is shared between G staking, AG and AQ pools with shares , and  respectively.

Defining:

• : Total G tokens in the AG pool, expressed as a proportion of outstanding supply of G.

• : Total A tokens in the AG pool, expressed as a proportion of outstanding supply of A.

• : Total A tokens in the AQ pool, expressed as a proportion of outstanding supply of A.

The allocation to G token staking, :

Noting the relationship between  and , and particularly if , .

The residual share, , is split between the liquidity pools:

For completeness:

3.3.5 Risky Premium Distribution

For , , we apply :

Taking  as a discount parameter:

The total Risky Yield tokens :

The allocations of  are pro-rata to , , and thereafter:

1. Locked G: in proportion to G.

2. Locked AG, AQ tokens are allocated a weighting , depending on their time bucket :

   Where , are the proportion of all liquidity locked in each time bucket for AG and AQ respectively.

Thereafter each time bucket allocation is proportionate to LP holdings.

3.4 Interactive Model

This additional section is not is the original PDF version of the whitepaper. It presents an interactive model of the AAM where each parameter of interest can be adjusted by the reader.

In Section 3.4.1, a Carbon holder sells Carbon to the AAM in exchange for A tokens; from the point of view of the AAM, this represents a Carbon purchase. In Section 3.4.2, a holder of A tokens burns A tokens to buy Carbon from the AAM; from the point of view of the AAM, this represents a Carbon sale.

3.4.1 KLIMA Tokens Emitted When the AAM Purchases Carbon

In this section, the reader controls how many present-value tonnes of Carbon class  are purchased by the AAM. The number of A tokens emitted in exchange is calculated in real time. The price of Carbon class  is calculated by dividing the number of A tokens emitted by the AAM by the number of present-value tonnes of Carbon class  purchased by the AAM.

3.4.2 Carbon Sold by the AAM When it Burns KLIMA Tokens

In this section, the reader controls how many A tokens are burnt by the AAM. The number of liquid tonnes of Carbon class  sold by the AAM in exchange is calculated in real time. The price of Carbon is calculated by dividing the number of A tokens burnt by the AAM by the number of liquid tonnes of Carbon class  sold by the AAM.

4 Klima 2.0 Token Distribution

4.1 Planned Allocations

4.2 Programmatic Incentive Curve

The incentive issuance is built on a logistic function, , to generate total proportion of supply in issue. It is calibrated from the initial issuance at TGE  and the inflection point time  where 50% of G token incentives have been released.

Setting  from the initial supply parameter:

With at time point :

Giving supply function as:

set at 7.0% and  at 24 months:

4.3 Incentive Allocations

The relative utilisation measurement factor  is calculated as follows.

Defining initially:

• : Total G tokens staked expressed as a proportion of circulating supply, .

• : Total G tokens held in the AG pool expressed as a proportion of circulating supply, .

Where if , otherwise:

The absolute utilisation parameter  is defined as  if , otherwise:

Incentives  are allocated as follows:

Treasury

The allocation to the Treasury  is the imbalance generated from :

Post Treasury

The residual post Treasury allocation is shared four ways within 2 buckets:

1. A Bonds & G Staking

   Where  is the proportion of A tokens that are staked for Bonds (as defined previously in Section 3.1):

   1. A Bonds, :

   2. G Staking, :

2. Liquidity

   With , , as defined in Section 3.3.4:

   3. AG Pool :

   4. AQ Pool :