This post will provide the backstory behind the Early Hammer Manipulation strats and how the technique was developed, will give an overview of how it works and all the parts of the game involved, and introduce the high level technical details that make it possible.
Analysis of the random number generation present in Super Mario Bros. 3 is desirable due to the amount of places in the game that change the course of a playthrough based on a number chosen from the random number array. The speedrunning community has done considerable work to avoid needless interactions with hammer brothers and other elements controlled by random numbers, but as of the time of this writing, a lot of interactions are still left up to chance and no in-depth research has been published on the random numbers used by Super Mario Bros. 3.
Early Hammer is the name given to the scenario in World 2 when the Boomerang Brother that holds the hammer moves across the 2-sun level and possibly even 2-3 in order for the player to get a hammer before playing those levels. If the hammer is used on the block below 2-3, up to three levels can be skipped (2-3, 2-sun, and 2-5), saving a speedrunner roughly a minute.