Yup, The World Reflected in the Eyes of the Girl who Looks Up at the Sky is KyoAni alright. You recognise their style right away. Looks like this is part of their "Munto" series which have been going on for some time...

And what is it with Japanese and long titles? More attention catching? Not sure what the shortened name for this is but suggestions seem to be "KaraAge (空あげ)", kara being the alternative pronunciation for the title's first Kanji and means empty instead of sky. Or it could also be "SoraAge Shoujo". Seems unsettled yet but I think the latter sounds better.

Sora o Miageru Shoujo no Hitomi ni Utsuru Sekai Episode 1
To Know

Thirteen year old Yumemi Hidaka wakes up watching a giant stone pillar falling from in the skies and is it lands, a tidal wave is created in the sea. She pulls back the curtains to find it was pouring rain but she liked rainy days because everyone saw the sky the same way.

A news report was talking about the sudden mysterious tidal wave that occurred at Kiisuidou which catches Yumemi's attention during breakfast. Finishing up, she leaves the house but was sad the rain had already lifted. As she steps out the door opening up her umbrella, the world around her suddenly disappears leaving only a reflective ground covered in water.

She walks on with a surprised look on her face until she hears the calling of her friends Suzume and Ichiko. Heading off to school, Ichiko asks Yumemi if she continues to see floating islands in the skies. She looks up from under her umbrella and quietly answers yes. She was beginning to think there was something wrong with herself but Ichiko tries to comfort her saying it doesn't matter.

As they stop by the road waiting to cross, Yumemi notices something and suddenly the world changes again. This time she finds a fiery haired young man had landed before her. He claims she was the destined girl and demanded she lent him her power. She backs off a little, frightened as to who this stranger was. He steps forward insisting there was no time but is repelled by a space-time barrier. Yumemi is woken up by Ichiko again.

The young man's name was Munto and was the King of the Magical Kingdom. The world was at the brink of destruction and he was willing to travel to the Lower World to find a power that could save it. He thinks back to the time he met with the observer and Outsider Gass who had reminded him it was a forbidden act and it will not be easy to do what he trying to do. However, he lets him go because he saw no reason to protect the rules in this falling world. He is curious as to what Munto saw in his vision. Munto turns away and answers he saw a girl. He wasn't going to let the world fall and he was determined to break through the barrier to obtain the same power the Outsiders could make use of.

At another place, the Allied Forces were having a meeting as to how to save their world by preserving what's left of the Arkt energy that kept their world in balance. They had come to the decision to eradicate the Magical Kingdom as they decide they are the ones responsible for the sudden decrease of Arkt. However, Gass was preventing their forces advancing. At this rate, even more of the Arkt energy will be depleted. They do not understand why the neutral Outsiders are suddenly helping to protect the pillars that held the Magical Kingdom in place.

The Allied Forces are even more surprised when they learn that Munto had descended to the Lower World where Arct energy was so low, it could lead to his death. His death was inevitable of course. They decide to leave him to die that way but, Commander Guntarl suggests they sent a warrior formed from the very powers of Arct during the Age of Gods to go after him just to make sure.

Back in the Lower World,Yumemi was still bothered about what she saw. Ichiko believes her but tells her not to think about the dangerous man. They leave for their PE class and while they were waiting for their turn in the volleyball match, they talk about Suzume's boyfriend. There were rumours he was a delinquent and was responsible for the injuries of a PE teacher. Worried Suzume was being fooled by him, they decide to pay him a visit and see just what kind of person Kazuya really was.

Thoughts

The first soundtrack after the opening sounded a bit like the Laputa theme song. Nice catchy theme songs but can't say the same for the lyrics sadly. I like the tranquility of the show so far. Feels a bit like El Hazard so the setup is kind of familiar too.

Yumemi's character design reminds me of Mikuru from Suzumiya Haruhi.