Bitcoin's complex architecture is underpinned by various encryption processes and mathematical formulas, including the use of integers and Poisson distribution. The use of integers, or whole numbers and their negative counterparts, ensures that all computational devices can synchronize more effectively and agree on specific network changes, while also being faster and less prone to error than floating-point numbers. Bitcoin's mining difficulty and block rewards also utilize integers, and transaction inputs and outputs are regulated by them as well. Poisson distribution, a mathematical formula developed in 1837, is used to regulate block time consistency, ensuring that blocks are discovered approximately every 10 minutes. Satoshi incorporated a difficulty setting every 2,016 blocks using the formula to maintain the rough average of 10-minute block intervals. These mathematical mechanisms and encryption schemes, along with others such as proof-of-work, Merkle trees, and cryptographic hash functions, ensure the accuracy, consistency, and efficiency of the Bitcoin system. (Bitcoin.com)