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One of the major outstanding foundational problems about boolean functions is the sensitivity conjecture, which (in one of its many forms) asserts that the degree of a boolean function (i.e. the minimum degree of a real polynomial that interpolates the function) is bounded above by some fixed power of its sensitivity (which is the maximum vertex degree of the graph defined on the inputs where two inputs are adjacent if they differ in exactly one coordinate and their function values arearXiv:1511.07729v1 fatcat:3qcibujuczhhxhenplqsgrev7u