Heaven's Lost Property/WMG

The angel/celestial maiden who bathed in the Satsukitane family's hot spring was an inhabitant of Synapse.
This could explain why all sorts of natural disasters happened to the town when anybody else used it; since the inhabitants are a bunch of assholes ruled by a Complete Monster, enacting a Disproportionate Retribution seems right up their alley. Or even worse, it could be that they only had to cause disasters once and never again, then watch in amusement as the "downers" kill each other to make sure that the disasters never happen again. Seeing as how they get off on seeing death and destruction happen to the people on Earth, it isn't too far of a stretch to surmise that they would do it that way instead.

Eishirou Sugata is an inhabitant of Synapse.

 * The Master is going to be revoking his visa soon.
 * Jossed by Nymph. If one of the cast is coming from synapse and don't know it, my guess is Sohara.
 * Tomoki can only attract nonhumans, and that would almost be foreshadowing.
 * It could be Mikako, she certainly has the attitude for it.
 * For all her For the Evulz attitude she has not betrayed her friends. She will abuse them, but never to a deadly extent. The Master on the other hand...
 * I think you mean "never to a serious extent." That said, while she would indeed kill Tomoki or anyone else For the Evulz, you're right in that Mikako working for the Master would be a major shift in character (from Comedic Heroic Sociopath to Complete Monster).

Ikaros is going to have a Face Heel Turn
Tomoki is going to get a very big devolpment romantic wise with either Sohara or Nymph and her reactor hurts worse than ever. She is then tempted by The Master that he can stop the pain she agrees, out of jealously.
 * She is far too loyal to Tomoki for that to happen. More likely, she'd take the I Want My Beloved to Be Happy route or simply leave to be out of the way, only to be called back by Tomoki at the last minute.

Synapse's inhabitants are The Inspectors
The Inspectors are human aliens who had advanced technology. They come to Earth in Super Robot Wars 3 to 'discipline' the Earthlings back into line. Sounds a bit similar, no?
 * The Master is definitely a thoroughly-indoctrinated high-ranking official, much like Wendolo. He despises the common populace, but he either: A) Lacked the means to effectively waltz in and kill everyone (i.e. giant robots); B) Lacked the resources to simply waltz in and kill everyone; C) Thinks that waltzing in and killing everyone to be unrefined and beneath him. Due to the above reasons, he turned inwards and constructed Synapse using his own genius and available resources. His indoctrination finally backfires and he ends up hating all humanity instead of merely administering 'discipline' to them.
 * Daidalos, on the other hand, is something like Mekibos' case. She started with the same outlook with The Master, but eventually pulled a Heel Face Turn due to (possibly) Power of Love from the Downers' side. Her Heel Face Turn came out a bit late though, so she elected to stay in Synapse to keep The Master in line by proxy (Ikaros, Nymph, and Astraea; Hiyori is outside of her prediction but turned out good anyway).

Ikaros has Asperger's syndrome
Think about it. She has a strange attachment to that watermelon, has trouble expressing emotions, and she displays savant skills that put Kim Peek and Raymond Babbit to shame. Sounds autistic to me.
 * Ikaros is an artificial construct (though there is a possibility that she was based off an inhabitant of Synapse with the disorder). It was explicitly mentioned by Nymph in Forte that her low emotional processing ability was by design (compentsated by high combat and intelligence stats), as opposed to genetic mutation. This in combination with Japanese cultural disregard for the mentally handicapped makes this WMG unlikely.

Chaos, the loli angeloid will become mature angeloid in future chapter.

 * she, currently on chapter 48, is back at the sea "feeding". There is a chance that she will become like the one in Forte
 * she also get a shoes that's too big for her to wear that might be hinting she will grow bigger to the point the shoes will fit her

The angels of Synapse are Precursors
Angels were the first dominant civilization on Earth. Their technology eventually provided all their material wants, and their biology was enhanced to the point of functional Immortality. Their power was such that some of their conflicts resulted in the various extinction events of ages past. The greatest products of angelic technology were nigh-omnipotent reality-warping computers, which could be remotely called upon to perform most any task. To avoid abuse of this technology, each computer was tied to a set of divine rules controlled by a High Council.

Fearing cultural stagnation, most took to the stars seeking new knowledge and challenge. Others experimented with mortal avatars and eventually built the Synapse system, which would link their minds to avatars via induced dreams. Through these dreams the angels sought to experience mortal fears and joys. The avatars themselves were designed to look familiar while having only just enough power to survive their environment, and were basically mindless human bodies. Dreaming angels would be unable to access knowledge of their true natures, to better immerse themselves in their new lives. To avoid spoiling the illusion, Synapse and the rest of the angels' technology were sealed away from the rest of the world, where the avatars were free to roam.

Some issues with the system still remained; the dreaming angels couldn't help questioning where they came from or why they were so few. They may have not been able to breed; if they did, there could be problems finding a free angel to link with the baby. The angels eventually decided to create human civilization by giving some avatars sentience, as it was easier for them to accept being one of many. Their avatars could now give birth to normal children, and if an avatar died it would not be a long wait before it could be remade in a mothers' womb. Humans also dreamt up myriad creation myths; none true, but enough to take some bite out of the mystery.
 * Alternatively, the first human birth could've been an accident and things just took off from there. Bonus points if Daedalus was the first mother.

Tomoki is part Angel
It would help explain Tomoki's Nigh Invulnerability and the  in Chapter 53. Adding to this ...

Daedalus is Tomoki's Grandmother
Let's see, she keeps appearing in Tomoki's dream since he reminds her of his grandfather, Tomoki's grandfather appears too often to be insignificant to the plot, and we haven't seen Tomoki's grandmother, so...
 * Added to the context that Tomoki's Grandfather slept with all the girls in the world , so...
 * Maybe she enter Tomoki's grandfather's dream, and he did that with her.....

Sora No Otoshimono would end in a Bittersweet Ending
A manga made by the author is up. Title is [http://www.mangafox.com/manga/daisuki_desu_mahou_tenshi_kosumasu/ 'Daisuki Desu! Mahou Tenshi Cosmos']. It is shown here that most of the villages have been eradicated for no apparent reason and maybe connected to the Synapse incident. By the way  Thus to further explanation that Tomoki's hometown maybe the one.
 * Alternatively, there was more than just one "Other World" while the synapse incident happened 6 years, it could be that it happened in HIS world. Maybe before the end of Otoshimono he was given a card that allowed him to enter and exit the world of Kosumasu. It could explain why he is missing from his room a lot. Spending time in the original world with his friends, but coming back to help fight in this world, since the same 'destroy humans' is happening.

Tomoki is afraid of having sex
For all his pervertedness, Tomoki is actually quite terrified at the thought of going further than peeping and groping and actually doing the deed with any of the girls. This is why he panicks at the thought of Ikaros joining him in the bath (if it were just chivalry, he could have politely turned her down instead of whacking her) and part of why he hasn't gotten it through his head that he has three angeloid pets who would do anything he asked of them (and, in fact, are getting really tired of waiting for him to ask for something).
 * Given that the angeloids have some extreme strength, they may just break his bones if it gets too intense.


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