Meaning of the underlined sentence

Meaning of the underlined sentence

The passage below is from A History of the Index by Dennis Duncan.

Looking back to the Library of Alexandria, it cannot be said for certain that the principle of alphabetical organization was the invention of Callimachus or his colleagues at the Mouseion. Nevertheless, given the lack of earlier evidence, and the appreciable requirements imposed by the accumulation of information on an unprecedented scale, it seems, in Lloyd Daly’s measured phrase, ‘a reasonable and attractive hypothesis’. The vastness of the Library – ancient Greek Big Data – necessitated a major technological shift: from abecedarium to alphabetical list, from knowing alphabetical order to using it. The use of alphabetical order represents a huge intellectual leap: the rejection of the intrinsic characteristics of the materials being organized in favour of something off-the-peg, something arbitrary. The payoff is a system that is universal, one that relies on information that any literate person will know already and that can be applied to anything, breaking it up into more manageable chunks. At its loosest, where ordering is only applied to the initial letter, the Greek alphabet provided for twenty-four separate buckets into which to divide the total, a significant improvement in the searchability of information. (This doesn’t only work for discrete information like lists. Another innovation at the Mouseion was to divide Homer’s epics, the Iliad and the Odyssey, into the twenty-four books in which we read them today. A work dating from slightly later states that this number was significant: the poems were divided ‘into the number of the letters of the alphabet, not by the poet himself but by the grammarians associated with Aristarchus’. Aristarchus was Keeper of the Library about a century after Callimachus.)

I don’t understand the underlined sentence.

Above all I don’t specify the meaning of ‘states’. It’s meaning can be ‘A condition or mode of being’. (Am I right?) But even it is, it’s just blind luck. I cannot get any meaning out of it. I thinks the real problem in figuring out the sentence is as follows:

It seems to be a sentence but seems to have no regular verb that corresponds to the subject ‘A work’. So the meaning of this not-seem-to-be complete sentence I cannot figure out.

Can you help me out with this mysterious-to-me-now sentence?

Thanks in advance.