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TeX flags overfull boxes when text cannot fit the line width. Raising tolerance can remove black rules, but looser spacing has typographic costs.
The goal is to configure TeX so that a positive \emergencystretch behaves as a binding upper bound on paragraph badness, preventing any overfull \hbox from being shipped out. In TeX82, \emergencystretch is consulted only after the first and second line-breaking passes fail, and it does not guarantee the elimination of overfull boxes; TeX still accepts a brea
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