After testing all possible options, Auto-Bracket ultimately returns sensible brackets for any given set of segments using standard NCL. Auto-Bracket's top choices for several example sets of model segments are shown in Figure . As expected, a convergent strategy (Figure ) generally scores better than a linear one (i.e., entirely N-to-C or C-to-N), but in many cases one of the many possible intermediate (or "semi-convergent") strategies is preferred over fully convergent. For example, a poor ligation site in the center of a protein should not be used for the final reaction between two multi-segment intermediates, but instead a lopsided bracket should be used so this problem reaction occurs earlier between less precious segments (Figure ); in terms of scores, the winning bracket applies path length penalties to as few segments as possible. In strategies with a mix of Ala and Cys sites, the requirement of all Ala ligations and desulfurizations to occur before native Cys ligations may outright forbid a convergent ligation order if Ala is centrally located (Figure ). Multiple adjacent Ala ligations can be performed and desulfurized simultaneously after the final one (Figure ), and thus the specific location of Ala sites is more important for bracket difficulty than the number of Ala sites. Finally, if Cys protecting groups must be removed in an explicit separate reaction step after NCL (which can be toggled in Auto-Bracket settings), steps will be added to the right half of many possible brackets and a linear (N-to-C) or semi-convergent bracket may score better than fully convergent (Figure ). Our bracket scores provide a mathematical basis for the intuitive logic of bracketology. When given the 7 segments previously used to assemble the largest protein published by our group, the 312-aa DapA, as well as the chemical limitations we had at the time (i.e., no one-pot desulfurization or deprotection steps), Auto-Bracket provides the strategy that was actually used (as shown in Figure ). Overall, Auto-Bracket provides a rapid alternative to manually drafting multiple brackets for comparison and mimics the process of an experienced protein chemist to assemble and compare multiple brackets.