Halo 4 Campaign Discussion- SPOILERS

Anybody else finish the campaign?

I think I get the main points of the campaign with the Librarian, Didact and the Composer, but I'm scratching my head about what happened with Cortana at the end. Where is she?

I'm going to throw out some takeaways from the campaign. Please correct me where I'm wrong. I know most of this is spelled out in the books, and the game did a nice job bringing it all together.

Didact

Annihilated the humans 100,000 years ago. Wanted to completely destroy them but the Librarian wouldn't allow it. Didact was placed in a Cryptum for his "crime".

Prometheans

Humans modified by the Didact. The bipeds are chamanune while the ones that run around like dogs are the hamanunes or florians.

Librarian

Indexer of all civilizations. She explained to Master Chief that everything he is, including his armor and Cortana was planned out hundreds of thousands of years ago to prepare humanity to take back the mantle.

The Composer

The tool the Librarian uses to plan and shape civilizations. Also, can convert living tissue into an ancilla, which is how Didact converted humans into Prometheans.

Overall

So the Didact is saying Humanity is the greatest threat in the universe because the Librarian, using the Composer, has written their song, which is to reclaim the mantle once held by the Forerunners. That's why Master Chief and other humans are referred to as Reclaimer. The Didact disagrees that the Humans should be given the Mantle, maintaining that the Forerunners should retain it.

Is that right?