This new approach aims for the quickest possible consensus by directly targeting the Directed Acyclic Graph (DAG) width to set difficulty levels. The core insight is that an optimal DAG width of 1 enables unanimous agreement among nodes regarding the system's state. This condition is achieved when a block becomes the sole link between two generations of blocks within a single latency period, effectively ensuring its uniqueness and facilitating faster consensus.

The methodology for measuring DAG width is straightforward, focusing on counting a block's parents and aiming for a fixed number. Surprisingly, setting the target to two parents yields the most efficient consensus, minimizing the standard deviation of parent numbers to one. This simplicity contrasts sharply with other DAG-based systems that require intricate analysis of extensive block trees. Moreover, it has been discovered that targeting exactly two parents leads to consensus being reached approximately 2.71828 times the defined latency period. This factor intriguingly mirrors the ratio of total blocks to consensus blocks, suggesting an underlying mathematical relationship that merits further investigation.

The difficulty adjustment algorithm (DAA) introduced operates by modifying difficulty based on the average number of parents over recent blocks. If this average exceeds two, the difficulty increases, and conversely, it decreases otherwise. This mechanism ensures adaptability and maintains the desired network behavior over time. Simulations of this algorithm have demonstrated its effectiveness, showing a near-ideal mean standard deviation and a consensus speed multiple closely aligned with theoretical expectations.

The comparison between this DAG-based consensus mechanism and the Avalanche protocol reveals a shared foundation in how both systems manage waste and secure decentralization. Both approaches incur a form of 'waste'—be it through network messages or hashing—to achieve consensus, underscoring the inherent costs of distributed security. This parallel highlights a critical consideration in blockchain technology: the balance between efficiency, security, and decentralization. Ultimately, this advancement presents a promising direction for blockchain consensus algorithms, potentially offering a more efficient alternative to existing methodologies.