My question is regarding the ending of Vivy-Fluorite Eye's Song. I will put it beneath a spoiler block just in case someone accidentally clicks on this going through the tag.
At the end of Vivy-Fluorite Eye's Song we watch Matsumoto save Vivy when the final satellite is going to crash into her. We see that the explosion has damaged Matsumoto and the light fades out of Vivy's eyes.
After the ending credits, we see that Matsumoto is waking up Vivy who is now wearing a short haircut and a different outfit. Matsumoto tells her that her name is Vivy and that her missions to make everyone happy through her singing.
Are these two AIs Vivy and Matsumoto as we know them or are they recreations of them based on saved data? My guess are that these are re-creations since their original "bodies" were destroyed. However, there are more questions with that assumption. If they are re-creations based on saved data, how did they re-create Matsumoto? Are we to assume Yui knew of backup that Professor Matsumoto had? Since Matsumoto was created for the Singularity Project, why would there be a backup? Continuing on the topic of Vivy being a recreation, is it similar to where she had alter ego Diva up front or is this a brand new AI that is being crafted around the Vivy identity?