Service Proofs as Edge Attributes

Service proofs verify that a transaction has been successfully completed between a buyer and a provider. In the Local Protocol, these proofs can take the form of pin exchanges, location proofs, or other evidence of service completion. Service proofs enhance the reliability of the transaction graph, ensuring that rewards are allocated for users performing real transactions and not fake transactions.

When available, service proofs can be integrated into the graph value calculation, increasing the weight of the corresponding edge for the transaction, making it more valuable to the network.

Service Proofs in the Adjacency Matrix

Each edge $(u, v) \in E$ in the graph has a weight $w_{uv}$ representing the cumulative fees or value from transactions between producer $u$ and buyer $v$. When a service proof is available, we adjust the edge weight to reflect the increased confidence in that transaction:

$$w_{uv} \leftarrow w_{uv} + b,$$

where $b$ is the boost provided by the service proof.

Alternatively, in terms of the adjacency matrix $\mathbf{A}$, we update the entry:

$$A_{uv} \leftarrow A_{uv} + b.$$

This adjustment increases the significance of the edge $(u, v)$ in the calculation of EC.

Impact on Eigenvector Centrality and Rewards

By increasing the weight of the edge $(u, v)$, both nodes $u$ and $v$ receive a higher EC score due to their strengthened connection. This boost is again propagated through the network.

Higher EC scores translate into increased graph values $G_u$ and $G_v$, which are used to calculate block rewards. Therefore, providing service proofs directly benefits the involved parties and indirectly enhances the trustworthiness of their neighbors.

In the next EC calculation, both $x_u$ and $x_v$ will increase more than they would have without the proof. This results in higher rewards for both parties and increases their attractiveness as transaction partners in the network; transacting with high EC nodes boosts ones own EC.

Key Concepts#

• Transaction Verification: Confirms that services have been provided as agreed.
• Graph Integration: Boosts graph value, aligning rewards with verifiable transactions.

Next Steps#

Next, we discuss why modeling proofs in Local Protocol is more cost effective than opinionated or narrow DePIN architectures, and argue that DePIN requires Local Protocol to unlock new use cases that are limited by the availability or cost of proofs. We do this by modeling proofs as probabilities.