WMG / Maison Ikkoku

Yotsuya is Golgo 13

Think about it: He has a job that requires him to work odd hours and which he can not reveal anything about. He demonstrates remarkable stealth when he wants to, and is never at a loss for words.

And look at those eyebrows! It's staring you right in the face!

Yotsuya is a Time Lord.

IT EXPLAINS EVERYTHING!

• How does Yotsuya manage to live (and, presumably, pay the rent) without any signs of steady employment, or even a normal daily routine? Obviously, he completes his business by using his Time Lord powers, leaving the other residents of Maison Ikkoku none the wiser.
• Room #4 is his TARDIS. This is why, on the rare occasions the inside of his room is seen (such as the egg episode and the Yagami tutoring episode), it looks completely different...they were just two parts of the larger complex.
• Time Lords have a longer than average lifespan. This explains how, when Kentaro found the photograph album, there were pictures of Yotsuya going back to the 19th century, yet looking completely the same. (What, you actually believed the explanation that it was his family members? No two people, however related, resemble each other quite that much.)
• Telepathy is another power of Time Lords. How else could Yotsuya know the exact moments to do a Stealth Hi/Bye and catch Godai in a blackmailable state, often in the middle of the night or in completely unrelated parts of town? This happens way too often to be coincidence.
• Like the Doctor, Yotsuya's true name is too bizarre or unpronouncable for daily life. Hence his use of a simple pseudonym, and his lack of interest in giving out a first name. (Alternately, Yotsuya's statements that his first name "is spelt like X and pronounced like Y" are actually true, and it's just that humans haven't figured out the complexities of the Gallifreyan language that would make this intelligible.)
• From The Other Wiki: "Time Lords are an aloof people, with a society full of pomp and ceremony." Sound like any traditional clothes-wearing, formally-speaking, haiku-quoting person we know?
• Finally, a travelling Time Lord needs a pretty Companion...Yotsuya has Akemi. Or at least, he thinks he does. Unfortunately for him, she's also working for the Master...

Yotsuya is Moon Knight.

• Moon Knight has several different names when out of costume. Yotsuya also goes by many names. Wouldn't be suprised if "Fist of Khonshu" or "Yitzak Topol" was among them.
• Yotsuya's past is just as confusing as Moon Knight's. Was he working for The Commitee or just pretending to.
• Moon Knight (Marc Spector) was a former C.I.A operative. Yotsuya is heavily suspected to be a government agent

Ibuki was an attempt to quietly and indirectly replace Kozue as Kyoko's main romantic rival for Godai in the 2nd half of the series to make Kyoko look better.

Kozue is a plucky endearing nice girl who became Godai's "sort-of girlfriend" over the course of the first half of the series. Of course its been often said that Godai still tries to pursue Kyoko but just couldn't have the heart to break it up with Kozue since she is so nice. However while Godai still pined for Kyoko he does enjoy his time with Kozue as well. However this is a problem since Godai and Kyoko are supposed to be the Official Couple and since Kozue is supposed to be only a Romantic False Lead.

But here is the thing, Takahashi made Kozue to be a bit too nice of a Romantic False Lead as Kozue is nicer, and more open about her feelings to Godai than Kyoko was. (In which even the show fully acknowledged her as a Romantic Runner-Up to Godai.) In which there was a considerable danger than viewers would want Godai to go with Kozue than Kyoko instead (in which to certain viewers the damage has already been done). But Takahashi wants to avoid that certain pairing issue that happened in Urusei Yatsura but seemingly tries to avoid the Derailing Love Interests trope as well for the story so what to do?

Basically Takahashi quietly wrote Kozue off as being Demoted to Extra over the remainder of the 2nd half of the series and introduced Ibuki Yagami. Ibuki is a bratty clingy High School girl who wishes to deem herself to be Godai's One True Love and deems herself to be Kyoko's rival for Godai's love. Though unlike Kozue the plot is very open about how Ibuki never had a chance with Godai in which Godai openly says he has no intention in loving her back but does try to reason with her though. So basically to make a long story short Takahashi tried to quietly replace a nice and endearing Romantic False Lead with a bratty and clingy Stalker with a Crush. Granted over the course of the series Takahashi does try to soften up Ibuki's character so this purpose won't be too obvious but still Ibuki was there to make sure people wanted Godai to go with Kyoko anyways.

Yotsuya works as one of Shutaro Mendo's estate guards.

The Ikkoku and Urusei Yatsura manga were running at the same time, and MI characters frequently popped up in the background of various UY manga and anime scenes.

Yotsuya works for the Incubators, or is an Incubator in disguise.

It would explain his cryptic, slinky manner and possible Reality Warper abilities, as well as how he was possibly alive in the 19th century. He or his fluffy white superiors are here to contract the depressed Kyoko or jaded alcoholic Akemi.

• The Witch Roberta (seen in Madoka Episode 10) might have been Akemi, given how she gives off the appearance of a hard-drinking hostess who's frequently harassed on the job.
• And speaking of Akemi...

Homura is an illegitimate daughter of Akemi.

She didn't think she could properly raise a child, and so she gave her up to an orphanage using her given name for Homura's surname. And perhaps due to drinking while pregnant, her daughter would grow up with many health problems. Homura would grow up thinking she was unwanted, which of course had all the consequences you can think of.

• One problem with this is that Maison Ikkoku takes place during the time of its original release in The '80s, whereas Madoka Magica was relased in 2011, and Homura and the rest of the main cast are only 14. Perhaps MI and Madoka take place in an Alternate History where the 1991 economic crash that ended Japan's '80-era bubble economy never happened, and the country's wealth and technological output continued on to a degree that by about 2000 they and possibly the rest of the world already had 2010's-era technology (this might even explain the vaguely 20 Minutes into the Future look of Madoka 's cityscape and technology). Therefore, Akemi could've given birth to Homura in 1986 (the year the anime debuted), thus setting Madoka in 2000 which again, could tie in with Madoka 's millennarian, apocalyptic overtones.