# WorkLock¶

## Overview¶

WorkLock is a novel, permissionless token distribution mechanism, developed at NuCypher, which requires participants to stake ETH and maintain NuCypher nodes in order to receive NU tokens.

WorkLock offers specific advantages over ICO or airdrop as a distribution mechanism, chiefly: it selects for participants who are most likely to strengthen the network because they commit to staking and running nodes.

The WorkLock begins with an open bidding or contribution period, during which anyone seeking to participate can send ETH to the WorkLock contract to be escrowed on-chain. At any time during the contribution period, WorkLock participants can cancel their bid to forgo NU and recoup their escrowed ETH immediately. Once the contribution period closes, the WorkLock contract does not accept more bids, but it will still accept cancellations during an additional time window. At the end of this cancellation period, the claiming window opens and stake-locked NU token allocations can be claimed by participants. Stake-locked NU will be distributed according to the following principles:

• All of the tokens held by WorkLock will be distributed.

• All bids must be greater than or equal to the minimum allowed bid.

• For each bid, the surplus above the minimum allowed bid is called the bonus; all bids are composed of a base bid (fixed minimum bid) and a bonus bid (variable amount).

• Each bidder will receive at least the minimum amount of NU needed to stake.

• Once all bidders have been assigned the minimum amount of NU, each bidder with a bonus will receive a portion of the remaining NU, distributed pro rata across all participants, taking into consideration only their bonus ETH amounts.

• If the resulting NU distributed to a bidder is above the maximum allowed NU to stake, then such a bidder has their bid partially refunded until the corresponding amount of NU is within the allowed limits.

Finally, if WorkLock participants use that stake-locked NU to run a node, the NU will eventually unlock and their escrowed ETH will be returned in full.

## Hypothetical Bidding Scenarios¶

Note

To reduce complexity, calculations are performed in a step-wise manner which may lead to minor rounding differences in the determined values.

For each scenario, assume the following hypothetical WorkLock properties:

1. WorkLock holds 280,000,000 NU tokens and the minimum bid is 15 ETH.

2. The minimum amount of NU required to stake is 15,000 NU and the maximum stake size is 4,000,000 NU.

3. The total number of bidders is 1000 bidders (including you) with a total of 50,000 ETH committed (including your bid).

4. For our purposes, a whale bid is a bid that causes the calculated stake size to be larger than the maximum stake size (4,000,000 NU).

### Scenario 1: Resulting stake size does not exceed maximum stake size (no whale bids)¶

You submit a bid of 22 ETH i.e. 15 ETH minimum bid + 7 bonus ETH.

How many NU tokens would you receive?

• Each of the 1000 bidders (including you) would receive at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum distribution is

$280,000,000 NU - (15,000 NU \times 1000 \,bidders) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum bids) is

$50,000 ETH - (15 ETH \times 1000 \,bidders) = 35,000 ETH$
• Your bonus portion of the bonus ETH supply is

$\frac{7 ETH}{35,000 ETH} = 0.02\%$
• Your portion of the remaining NU is

$0.02\% \times 265,000,000 NU= 53,000 NU$

Total NU tokens received = 15,000 NU + 53,000 NU = 68,000 NU

### Scenario 2: Resulting stake size exceeds maximum stake size (1 whale bid)¶

You submit a bid of 715 ETH i.e. 15 ETH minimum bid + 700 bonus ETH.

How many NU tokens would you receive?

• Each of the 1000 bidders (including you) would receive at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum distribution is

$280,000,000 NU - (15,000 NU \times 1000 \,bidders) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum bids) is

$50,000 ETH - (15 ETH \times 1000 \,bidders) = 35,000 ETH$
• Your bonus portion of the bonus ETH supply is

$\frac{700 ETH}{35,000 ETH} = 2\%$
• Your portion of the remaining NU is

$2\% \times 265,000,000 NU= 5,300,000 NU$

However, the total amount of NU tokens to receive is 15,000 NU + 5,300,000 NU = 5,315,000 NU which is greater than the maximum stake amount (4,000,000 NU). Therefore, the amount of NU tokens distributed to you needs to be reduced, and some of your bonus ETH refunded.

• Typically the calculation for the NU received from the bonus portion is

$\frac{\text{your bonus ETH}}{\text{bonus ETH supply}} \times \text{remaining NU tokens}$
• The additional complication here is that refunding bonus ETH reduces your bonus ETH AND the bonus ETH supply since the bonus ETH supply includes the bonus ETH portion of your bid.

• A more complicated equation arises for the bonus part of the calculation, where x is the refunded ETH:

$\text{stake size} = \frac{\text{(your bonus ETH - x)}}{\text{(bonus ETH supply - x)}} \times \text{remaining NU tokens}$
• Since you will receive a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, the most you can receive from the remaining NU is

$4,000,000 NU - 15,000 NU = 3,985,000 NU$
• Therefore using values in the equation above yields

$3,985,000 NU = \frac{700 ETH - x ETH}{35,000 ETH - x ETH} \times 265,000,000 NU$
• Reorganizing the equation

$\begin{split}x &= \frac{700 ETH \times 265,000,000 NU - 35,000 ETH \times 3,985,000 NU}{265,000,000 NU - 3,985,000 NU} \\ &\approx 176.33 ETH\end{split}$
• Therefore, your final bonus bid is

$700 ETH - 176.33 ETH \approx 523.67 ETH$
• Your portion of the bonus ETH supply is

$\frac{523.67}{(35,000 ETH - 176.33 ETH)} \approx 1.504\%$
• Your portion of the remaining NU is

$1.504\% \times 265,000,000 NU \approx 3,985,006.46 NU$

Total NU tokens received ~ 15,000 NU + 3,985,006.46 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH

### Scenario 3: Resulting stake size exceeds maximum stake size (2 whale bids)¶

Someone else submitted a bid of 715 ETH (15 ETH + 700 bonus ETH); we’ll call them whale_1.

You submit a bid of 785 ETH i.e. 15 ETH minimum bid + 770 bonus ETH; you are whale_2.

How many NU tokens would you receive?

• Each of the 1000 bidders (including you) would receive at least the minimum NU to stake = 15,000 NU

• Remaining NU in WorkLock after minimum distribution is

$280,000,000 NU - (15,000 NU \times 1000 \,bidders) = 265,000,000 NU$
• Bonus ETH supply (i.e. total ETH not including minimum bids) is

$50,000 ETH - (15 ETH \times 1000 \,bidders) = 35,000 ETH$
• Your portion of the bonus ETH supply is

$\frac{770 ETH}{35,000 ETH} = 2.2\%$
• Your portion of the remaining NU is

$2.2\% \times 265,000,000 NU= 5,830,000 NU$

However, the total amount of NU tokens to receive is 15,000 NU + 5,830,000 NU = 5,845,000 NU which is greater than the maximum stake amount (4,000,000 NU).

• From the previous scenario, the equation for the bonus part of the calculation is as follows, where x is the refunded ETH

$\text{stake size} = \frac{\text{(your bonus ETH - x)}}{\text{(bonus ETH supply - x)}} \times \text{remaining NU tokens}$
• Additionally, there is more than one whale bid, which would also cause the bonus ETH supply to reduce as well

• Instead the following whale resolution algorithm is employed:

1. Select the smallest whale bonus ETH bid; in this case 700 ETH from whale_1 < 770 ETH from whale_2

2. Equalize the bonus ETH whale bids for all other whales (in this case, just whale_2 i.e. just you) to be the smallest whale bonus bid i.e. 700 ETH in this case

3. Since your bonus ETH bid is > 700 ETH, you will be refunded

$770 ETH - 700 ETH = 70 ETH$
4. This reduces the resulting bonus ETH supply which will now be

$35,000 ETH - 70 ETH = 34,930 ETH$
5. We now need to calculate the bonus ETH refunds based on the updated bonus ETH supply, and the maximum stake size.

6. Remember that everyone receives a 15,000 NU minimum, and the maximum stake size is 4,000,000 NU, so the most you can receive from the remaining NU is

$4,000,000 NU - 15,000 NU = 3,985,000 NU$
7. Since we have multiple bidders, our equation is the following , where n is the number of whale bidders

$x = \frac{\text{(min whale bid} \times \text{token supply - eth_supply} \times \text{max stake)}}{\text{(token supply - n} \times \text{max stake)}}$
8. Plugging in values

$\begin{split}x &= \frac{(700 ETH \times 265,000,000 NU - 34,930 ETH \times 3,985,000 NU)}{(265,000,000 NU - 2 \times 3,985,000 NU)} \\ &\approx 180.15 ETH\end{split}$
• hence each whale gets refunded ~ 180.15 ETH

9. Therefore,

• whale_1 is refunded ~ 180.15 ETH

• whale_2 (i.e. you) is refunded ~ 180.15 ETH + 70 ETH (from Step 3) = 250.15 ETH

10. Based on the refunds

• The bonus bids for the whales will now be equalized:

• whale_1 bonus bid = 700 ETH - 180.15 ETH = 519.85 ETH

• whale_2 bonus bid = 770 ETH - 250.15 ETH = 519.85 ETH

• The updated bonus ETH supply will be

$35,000 ETH - (180.15 ETH + 250.15 ETH) = 34,569.70 ETH$
11. Each whale’s portion of the bonus ETH supply is therefore

$\frac{519.85 ETH}{34,569.70 ETH} \approx 1.504\%$
12. And each whale’s portion of the remaining NU is

$1.504\% \times 265,000,000 NU = 3,985,600 NU$

Total NU tokens received ~ 15,000 NU + 3,985,600 NU (rounding) ~ 4,000,000 NU, and refunded ETH ~ 176.33 ETH

Note

In Scenarios 2 and 3, you will notice that the bonus ETH supply was reduced. This produces a very subtle situation - for previous non-whale bids (bids in the original bonus ETH supply that did not produce a stake larger than the maximum stake) their bids remained unchanged, but the bonus ETH supply was reduced. This means that some bids that were not originally whales, may become whales once the bonus ETH supply is reduced since their proportion of the bonus pool increased. Therefore, the whale resolution algorithm described in Scenario 3 may be repeated for multiple rounds until there are no longer any whales. To keep the explanation simple, both Scenarios 2 and 3 ignore such a situation since the calculations become even more complex.