Amuria(f) is Aaeru's grandfather.Two of the big mysteries that were Left Hanging at the end of the series were the identity of Aaeru's grandfather and the fate of Sibylla Amuria, since they Never Found the Body. They seem to have somewhat similar facial structures, and share an obsession with the Emerald Ri Maajon and the "other world."
Dominura is Onashia.This seems less likely, but both have the same sparkly problem, and both were in Chor Dextra. An alternative but related theory makes Limone Onashia.
Aaeru and Neviril are Tempus and Spatium.They seem to exist in every time and place now, they're a pair just like Tempus Spatium, and Limone appeared to have started the whole phenomenon of identifying "aaeru" with the divine.
Anyone entering the Spring without clearly intending to be female will be assigned male.Inertia and fear would naturally cause people to tend to prefer to stay female, to the point that society enforces pre-feminist gender roles in order to get enough people to be men. And since someone who's indecisive on that point hasn't demonstrated a clear preference anyway, the interest of society is for them to help redress the potential man shortage.
The Spring is created from the same magical water as the Jyusenkyo springs from Ranma 1/2.Presumably, no tragic drownings were needed to activate these ones. Or the legends have long been forgotten.
The civilization of Simoun was the victim of a Gendercide.This results in there being no Y chromosomes left naturally in the population, so the spring tricks the body into thinking it is male so it develops the appropriate physical attributes and allows the reproduction of (female) children. However, this takes years, as shown by Waporif still having and eventually losing his breasts.
Helical motors are designed to harness Spiral EnergyFurthermore, the civilization that created the Simoun fought the Anti-Spirals and loss. The odd system of sex determination was created by a Lord Genome-like person in order to prevent the triggering of the Human Annihilation Program.
Simoun takes place about thirty thousand years after A Canticle for LeibowitzThe Quo Peregrinatur Grex led to the development of FTL and time travel. Eventually the human colonies on Daikuuriku were cut off from the rest in some disastrous war (a third Flame Deluge?), at the same time falling victim to Gendercide. They harnessed the power of the Spring (see above WMG) to trick some of their bodies into being male to ensure the survival of the species, a Divine boon that, combined with their dim memories of Roman Catholic ritual and space-faring civilisation, led to the creation of the Tempus Spatium religion (through the time loop engendered in the show). This explains, among other things, the Gratuitous Latin, the themes of recurrence, the existence and nature of Simulacran civilisation, and possibly even what happened in the past to destroy the Precursors.
Simoun Gems are computers.One of there purposes is to regulate the two Helical Motors the Simoun uses. This is why Simoun Gems aren't used in any of the crafts that run on a single motor.
Simulacrum did not get partitioned in the end.It just allied with Plumbum, which seems to harbour less fundamental ideological hatred for it than Argentum. This is why Vyuraf has to specify that he was born abroad to explain why Argentum is drafting him. Plus, the Plumbish Military Governor (the 'we were all maidens once' guy) was a defector to Simulacrum waiting to happen already.
The Spring is directly connected to Tempus SpatiumHence why Yun can apparently see the 'legendary pair' Dominura and Limone when she looks into it. The Girl Who Leapt Through Time associate time leaping with lavender. Amuria has lavender hair and escaped from almost certain death by traveling though time.
Mamiina became an archangel upon her deathThe mutiny of the Plumbish priestesses and outright Heel-Face Turn (Heel-Faith Turn?) of the Plumbish government are textbook eucatastrophe and required exploiting several flaws in the Arcus Prima superstructure that didn't seem to be there before (an open Maaju pool, breakable windows). The intervention of Mamiina's soul as opposed to someone else (or Tempus Spatium Herself) seems more likely given the Eye Catch that has her as an angel and the fact that, honestly, it just seems more Mamiina's style.
The helical motors contain Rynax entitiesIn a long-forgotten past, Rynax entities were locked inside spiral structures which were placed into round containers to facilitate making use of their special capabilities. Since Rynax are binary beings, always existing in pairs, placing two of them together will make sure they function at their best: one manipulating the temporal structure of space-time, and the other the time structure. The Rynax could have been forced into those spirals, or they could have done so out of their free will, so they can enjoy the "vast world" by interacting with the beings they find so fascinating. Perhaps Rynax even manipulate people unconsciously to place the right containers together. They work the best, or even at all, when the people manipulating their power care about each other as well, so the Rynax can project their pair-relationship onto them. When Dominura looks into one of the opened containers, she stares straight into the memories of a Rynax that may have been around for thousands of years already, which overloads her brain. The best way to unlock the Rynax powers is by performing the Emerald Ri Maajon. This not only causes a shift in time-space, but permanently imprints the Rynax pair-relationship onto the people performing it. This explains why Limone and Dominura form an inseparable bond, which resembles the one between Kurau and Christmas in Kurau Phantom Memory .