The launch of the SWAPP contract will kick off an initial 30 day phase during which users may send ETH (or any ERC-20 token traded on Uniswap V2) to the SWAPP contract in order to reserve SWAPP tokens. The tokens reserved can be minted by the users immediately following the end of the "auction phase", i.e. the start of day 31.
Each day of the auction phase will have a certain amount of SWAPP tokens that can be reserved by all those who deposit ETH to the platform on that day. Most days will have exactly five million SWAPP available, but the other days will have their available SWAPP amount randomly set within a predefined range. These random amounts will be determined by the contract shortly after the end of each random day, by leveraging the Provable (formerly called “Oraclize”) smart contract’s Random Datasource interface. The generated randomness is delivered on-chain in a trustless and provably cryptographically secure manner. For more detailed information about Provable, please read their random datasource white paper and their security deep dive.
Each day’s available SWAPP ends up getting split amongst the users who deposited ETH to that day, in direct proportion. In other words, a user that made a reservation on a particular LT day will later be able to mint the fraction of that day’s available SWAPP that equals the fraction of the day’s total ETH they personally sent in.