Djed is an overcollateralized crypto-backed algorithmic stablecoin contract on the Cardano network. It uses a reserve of ADA base coins and a Reserve Coin called Shen to maintain its peg to the USD and provide liquidity stability. By trading Shen, users can earn a share of transaction fees and contribute to maintaining the stablecoin peg ratio. Djed's algorithm is formally verified and uses mathematical theorems to prove its peg maintenance and stability properties. Shen holders are incentivized to provide liquidity, and Djed can be overcollateralized up to 8x, ensuring its sustainability. Users can mint DJED and SHEN directly from the platform or on any Cardano top DEXs.