Lore speculations

Hey Guys, just a disclaimer I have not played Halo wars 2, all this information comes from cut scenes of the campaign.
Major Spoilers ahead!!!

So during halo wars 2 the spirit of fire finds a halo in the foundry of the arc, as I haven’t played halo wars 2, I can only assume that this is alpha halo or instillation 04(c), (as it is the only halo that still needs repairs). The halo then deploys to its original position and along the way it is intercepted by one of cortana’s guardians.
Now this is where things get interesting.
Flash back to halo 5 legendary ending, we hear cortana humming while an instillation lights up, but it was ok, because cortana couldn’t activate it right?
Now that what I assume is installation 04c is in cortana’s hands as a guardian intercepted it it means that she is in ownership of it, and cortana also is in possession of instilation 04’s index which she used to activate 04b in halo 3.
so if i’m right the halo at the end of halo 5 was 04c, which cortana is in control of while she possesses a function activation index for this halo.

Oh damn… 0.0

Tell me what you think or point out any flaws, but i’m pretty sure this is what has happened as it all lines up