Which musical fragments are among the earliest examples of written music?

The Delphic Hymns are indeed recognized as some of the earliest surviving examples of written music from ancient Greece. Composed in the 5th century BCE, these hymns were intended for the worship of the god Apollo and are significant for their notation system, which reflects the musical practices of the time. The music written for the Delphic Hymns demonstrates an early attempt to notate pitch and rhythm, making it a crucial part of music history and the evolution of musical notation.

In the context of the other options, while the Pythagorean Hymns and Epic Chants refer to important aspects of ancient musical and poetic traditions, they do not have surviving notated examples that are as definitive in terms of being identified as written music. Lyric Poems, while they did contain musical elements, are primarily focused on the structure and themes of poetry rather than the notation of music itself. Thus, the Delphic Hymns stand out as a clear representation of early written musical notation.