Spirit of Fire in Halsey's Journal

So I got the Halo Reach Legendary Edition for Christmas and after playing through several rounds in the actual game proudly displaying my legendary flames I sat down and read through all of the contents of the Halsey journal.Some of the three page long equations(?) made no sense, however, what really left me confused was 2 mentions of the Spirit of Fire. These two seemed to be hinting at something but I don’t understand it. Halsey at that point shouldn’t really care because the Spirit of Fire has been lost for almost 20 years and will not resurface until 2559. So, why are these mentions of the Spirit of Fire in the journal?

Well, the first reference I saw was more about how Dr. Anders would be useful with the research Halsey was doing (even though they never got along). Couldn’t say for the second reference, but her reflecting on the few past “victories” against the Covenant may have made her think about the ship.