# $CARROT Distribution Model

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Last updated

The sale of Tokenized Recycling Credits and Tokenized Carbon Credits is the mechanism through which environmental work (avoiding pollution and preserving natural resources) is valued and rewards in $CARROT tokens can be distributed to recycling contributors. Finding an immediate buyer and pricing this work is accomplished through the use of Liquidity Pools and token pairs that provide liquidity and dynamic pricing for TRCs and TCCs, a unique solution created by and for DeFi (Decentralized Finance).

Each TRC and TCC is fungible and minted in 1 Ton increments following verification by Zero Waste Auditors. As soon as the tokens are minted they are sold in a TRC <> $CARROT or TCC <> $CARROT liquidity pool, where all of the Liquidity Providers become co-owners of TRC and $CARROT, in accordance with their stake within the Liquidity Pool. The price of each TRC and TCC is determined by the Automatic Market Maker (AMM) based on the balance of each token in the pool. When a TRC or TCC is sold (using an oracle price feed), its value is distributed in $CARROT tokens, split among all MassIDs it contains and then distributed to the correct participant wallet–IDs. When a TCC is sold, $CARROT is distributed to all TRCs it references. (This case is addressed in more detail after the following example.)

We will use a TRC example to help us walk through the remaining calculations. Let’s assume that a 1 Ton recycled glass TRC#1 is minted. It enters the queue of TRCs to be sold in the liquidity pool (earliest additions are sold first), and eventually TRC#1 is sold for $100.

V \: is \:a\: value \:function,\:and\: V(X) \:is\: the \:$ \:value of X

and Tr_(#1) is the TRC#1

V(Tr_#1)=$100

where N is the total amount of MassIDs in TRC#1

Tr_#1={M_0,M_1,...,M_N}

where M_0 is a MassID within TRC#1 (Tr_(#1)) with a weight of 10 kg

(.01)*(V(Tr_(#1)))=V(M_0)

(.01)*($100)=$1

V(M_0)=$1

For this example, we will assume that $1 USD is worth 100 $CARROT.

V(100 $CARROT)=$1

V(M_0)=$1=100 $CARROT

S_M \: is \: the \: total \: $CARROT \: value \: of \: a \: MassID \: (M_0 \: from \: the \: Tr \: TRC \: in \: this \: example)

thus \: S_M=100 \: $CARROT

S_M*P_0=x \:$CARROT ⇒P_0

S_M*p_1=x \:$CARROT⇒P_1

S_M*p_5=x \:$CARROT⇒P_5

**Note, the process for distributing $CARROT from the sale of a TCC** is very similar to that of a TRC, but with an added step. The value of the TCC is first split across the GasIDs that make up each TCC and then to each TRC that the GasID belongs to. In this way, the value of a TCC can still be tracked to each MassID that was certified-recycled by a Zero Waste Auditor.

$where...$

$And \: with \: the \: previous \: definitions \: of \: a \: TRC \: (T) \: we \: know \: that…$

$and \: that \:a \:MassID \: (M)…$

$M_0={\{glass,10kg ,CoC\}}$

$has \: a\: recycling\: chain-of-custody\: (CoC)\: containing \:the\: wallet-IDs \:of \:each\: participant$

$CoC={\{P_0,P_1,P_2,P_3,P_4,P_5\}}$

$P_0={i_0}=wallet–ID\: of\: waste \: generator$

MassID $M_0$weights 10 kg. This is 1% of the total weight of TRC#1, since each TRC packages 1 ton of mass. Therefore, the total value of the MassID $V(M_0)$ is 1% of the total value of the TRC V(Tr_#1).

TRC#1 was sold for $100, thus the value of the MassID $M_0$ is $1

Therefore, the allocation of $CARROT to the MassID $(M_0)$ is found to be 100 $CARROT. This process is repeated for every MassID so each is assigned a portion of the total value of the TRC.

The final step in the process, involves distributing this MassID value $V(M)$ throughout the chain-of-custody $(CoC)$. As explained previously, the recycling chain-of-custody $(CoC)$ contains a set of participant categories $(P_x)$ which each contains the wallet-IDs $(i_x)$ of all individuals or companies who fulfilled the category. Now we must introduce a new variable $(p)$ which is a weight value defined as the percentage of $CARROT that a participant category receives. So, the $CARROT given to each participant participant categories $(P_x)$ can be shown as:

$where...$

$and \: P_0 \: is \: the waste–generator,P_1 \: is \: the \: bin–custodian,...,P_5 \: is \: the \: recycling \: facility$

For example, if the percentage of $CARROT given to the waste-generator is 10% $(p=.10)$then the waste-generator $P_0$ receives100 * .10)=10 \:$CARROT for their contribution in recycling the glass in the MassID $M_0$ within the TRC TRC Tr_(#1). The diagram below helps to visually explain the distribution process.

Of course, the total value of every $p_x$ has to equal 1 representing 100% of the $CARROT value of the MassID being redistributed:

$\sum_{x=0}^5 (x=0)^5 p_x=p_0+p_1+ ...+p_5=1=100%$