Proof Of Study

Proof-of-Study is designed to address challenges in the digital course market, particularly the tendency for free courses to be hoarded without engagement. By aligning reward mechanisms with student incentives, it encourages consistent study habits over time. Students earn both a course completion certificate and financial rewards in the form of NTH tokens, similar to a scholarship, fostering genuine course engagement and completion.

Dynamics of Token Distribution

The tokens distribution follows the exponential decays law, i.e. a fraction of tokens is distributed in each unit of certificate. The number of tokens in fund allocated to the Proof-of-Study, denoted as $N(c)$, is a function of the number of completed certificates $c$ and the distribution rate $\gamma$. The functions that describe this behavior are

$$N(c) = N_0 e^{- \gamma c},$$

and

$$A(c) = \frac{dN(c)}{dc} =- A_0 e^{- \gamma c},$$

where $N_0$ is the total number of token for Proof-of-Study in unit of NTH, $A(c)$ is the activity of distribution in unit of NTH/certificate, and the activity starts with $A_0 = N_0 \gamma$. These two functions are showed by the figures.

The exponential decay law reduces the number of tokens by half for each full period, as highlighted by the graphic guide lines.

The exponential decay law reduces the activity by half for each full period, as highlighted by the graphic guide lines.

An signature of this function is that both number of tokens and activity are reduced by half for each period, known as the half-life. The half-life period is determined in units of competed certificates, i.e., both number and activity reduces by half after a certain amount of certificates are emitted. This quantity is given by

$$c_{ \textit{half-life}} = \frac{\ln 2}{\gamma}.$$

The value of \gamma\ is chosen based on the average number of certificates per year and the half-life.