Adjacent-suffix characterization of longest repeats

The length of a longest repeated substring equals the maximum longest-common-prefix length over adjacent suffixes in lexicographic order. Suffixes beginning with a fixed string form a consecutive interval: a string outside that string prefix software class differs earlier or ends sooner, putting it strictly to one side. Two occurrences of a longest repeated substring therefore bound an interval in which every adjacent pair shares that string prefix. At least one adjacent pair attains its length, and no pair can exceed the global maximum. This proves the result even when occurrences overlap; a text with fewer than two suffixes needs a separate empty-result convention.