May Indiana Jones claim copyright in the reconstructed text?

Situation: Indiana Jones finds the Dead Sea Scrolls in a cave, sealed inside amphorae. The scrolls have badly deteriorated so that what remains is a jumble of fragments, some legible and some not. Dr. Jones painstakingly tries to reconstruct the scrolls. He uses many types of evidence. For example, because he knows what size the scrolls were and roughly what their margins were, if there is a gap in the reconstructed scroll, he can deduce how big the word is, and come up with all the Hebrew words (or Aramaic or Greek if the scroll is in that language) that might fit. Dr. Jones is an expert in early Jewish sects, so he knows what type of wording is most likely. Then he can look at contemporary religious texts, at word frequency distributions, and predict which word fits the gap. If that makes sense linguistically and in the context of the religious text he is looking at, he can have greater certainty that the two fragments on either side are indeed from that particular scroll. Jones’ unparalleled linguistic, religious and archeological knowledge give him many clues like this—his colleagues describe his ability to synthesize all of these sources of information as nothing short of genius. At the end of two years of work, he claims to have the definitive “historical reconstruction” of the scroll.
Answer the following: May Indiana Jones claim copyright in the reconstructed text? Argue both sides. For each side, explain the analogies you would make, the doctrines you would invoke, and the particular precedents to which you would appeal.