Please read the synopsis before this review.
My watching experience with Vivy: Fluorite Eye's Song:

Every episode throws like 5 distracting incoherences at you. After contemplating about each of the issues, you'll come to realize that perhaps half of those do somehow make sense. You can appreciate the amount of thought, effort and detail that was put into the show thanks to the very process of evaluating the episodes after watching them. This was half of the fun and goes to show that there's enough to dig into. The other half of incoherences.... still don't make any sense.

Two examples:
Matsumoto is awfully irrational for the future ultra A.I. he's supposed to be.
Slight episode 3 spoiler:

Spoiler, click to view

The incident on the sunrise happens 24 hours earlier than in the original timline. Should he really be that surprised at the trajectory calculating a crash into a different place than before? Not only that, he literally asks "How did that happen?"

Of course I still enjoyed myself and that episode's ending probably remains the most emotional part of the show for me. I'm just left wondering what the point of these countless injections of human-like behaviour is. My guess, as the term already suggests, to make him more likeable as a character. It leaves a sour taste in my mouth to have them resort to cheap and off-putting tricks when they've proven to be able to brilliantly hint at character developments in a subtle way on many other occasions. You're better than this.

Major finale spoiler:

Spoiler, click to view

Why exactly did Dr. Osamu have to die? Vivy not saving him to immediately meet up with Toak didn't save much time. In the second timeline she spends time wondering what to do, explaining the current situation to the Dr., saving the random guy, etc. All of this could've been cut down to just saving him and gathering up with Toak immediately after.
No way this short amount of time spent saving him would've had significant impact on Toak's numbers for the final raid. After all, they already somewhat managed in the second timeline where Vivy had saved Dr. Osamu and wasted time. This is especially illogical because Osamu's death, with time travel now thrown out the window, subsequently marks humanity's final attempt.
Overall comes across as the desperate attempt to raise the stakes for the final episode in a show that doesn't even need it.
This may sound super negative but I'm just nitpicking a show I like.

All of this is excused however, since the focus does not lie on the overarching plotline, despite the series' seemingly bloated final arc. It seems hard to write a 13 episode story about a singing robot in the midst of a conflict between humanity and A.I. with everything making perfect sense anyway...... You can definitely look for and find some of the logic but don't overdo it.
Vivy: Fluorite Eye's Song juxtaposes the scale of the cinematic universe and it's huge stakes with the personal emotions it's trying to convey, and succesfully pulls it off.

Great production and sound design. The amount of action was perfect and didn't cause too noticeable consistency dips. Remarkable that this is WIT's supposed side project. Credit the actual people, not the studio though! When they did finally spoil us with fight scenes, they made sure for them to be top notch. We were showcased the talent and potential of animator as well as storyboarder Masahiro Tokumaru, who pushed the limits for what a dynamic battle between robots could realistically look like. I don't want to spoil the fight scenes but if you're sure you're not going to watch the anime, look them up online. He damn nailed them.

Give this show a watch. Good original anime are a rare sight and I can understand where people giving this an even higher score than me are coming from.