The above requires nodes to generate and merkleize a set of emission tokens they consider as required for a predefined period. The number of leafs depends on the expected winning frequency a node has during the epoch, which we denote as $F$.

Therefore, the number of leafs ($D$) that a node must generate is multiplication of:

• the length of the registration expressed as number of epochs ($R$),
• the expected winning frequency per epoch of a node ($F$),
• the maximal number of blending operations allowed per emission ($B$).

That is, $D = R * F*B$.

Moreover, a node must merkleize a set of all registered, stable and not expired quota registrations.

Implementation Complexity

The PoQ implementation complexity is relatively low as it requires only merkleization and a zero-knowledge proof. The PoQ implementation is (roughly) the same for both edge and core nodes.

Usage Complexity

The PoQ usage requires relatively high interaction but the cost of a construction of a proof is low. The interaction might be higher for nodes with higher stake as they need a higher quota, but

1. Core Nodes are obligated to perform PoQ registration every time they must refresh their PoV.
2. Edge Nodes are obligated to perform PoQ registration when they use up their quota or the validity of their PoQ expires.

We are not making any assumptions on the expiration time of the PoQ for edge nodes. However, we might consider having an expiration period for PoQ for two reasons.

1. We can reduce the storage requirement for PoQ and remove expired ones.
2. Expiration increases the cost of attacking the network (spamming) through the PoQ as an adversary cannot accumulate emission rights for an infinite period.

construction requires creation of a Merkle Tree with $2^{25}$ leafs. Each leaf corresponds to a single time slot and defines the chances a node has to propose a block. Therefore, it allows a node to use a single registration for the duration of $\approx 338$ days.

A single PoL requires node to generate $2^{25}\approx34*10^{6}$ leafs and to merkleize them. If the leaf length is an output of a SHA-256 hash function, then the node must generate and store $\approx 1$GB of data for a duration of the validity of the PoL (338 days).