Franken Fran/WMG

Professor Madaraki is somewhere in the mansion, suffering a Fate Worse Than Death

 * Ever since I thought of this, I can't get it out of my mind, and the fate gets worse each time I think about it. Evidence: (1) No one has seen Madaraki in an unknown time; (2) Madaraki is old and may have been approaching death; (3) Madaraki might have spent a lot of time near Fran; (4) Veronica doesn't appear to know where he is. (And maybe she was investigating Fran until Fran took her apart); (5) In a book that specializes in ironic hells, Madaraki has a big one coming; and (6) it would be the ultimate reveal if the book ever ends. The worst part of this is, that if Madaraki is suffering in a room someplace in the mansion, it logically should be worse than anything we've seen so far.

The girl the painter fell in love with in "A Beautiful World" is Adorea without her bandages and off the clock

 * Yeah it's probably not true. But I just think it would be sweet if Adorea could find love again after her own tragic back story.
 * It's not, as Adorea without her bandages= tentacled face.
 * Do remember that the girl the painter meets only looks human to him thanks to his altered vision. Her actual appearance is hinted to have tentacles too.
 * Hell, if you believe Grand Unifying Guesses, the girl the painter met may be Saya herself.

Professor Madaraki sent Gavrill to kill Fran and Veronica

 * Why? I don't know, but wouldn't Veronica, after spending all that time with Professor Madaraki, know his handwriting? She's his creation, and handwriting is Serious Business in Japan, so he may have actually sent Veronica the letter as a trap. Maybe he's actually the Big Bad from Sentinel 2.0, maybe he just hates them...Well, or, Gavrill is an expert forger.

Going off the above theory, Prof. Madaraki hates Fran and wants her killed.

 * Perhaps Prof Madaraki is disgusted at what Fran does and had a "My God, What Have I Done?" moment before abandoning her and sending his creations to destroy her.
 * Perhaps the sinking ship in the last chapter was caused by Madaraki to do just that.

Fran is actually the daughter of Professor Stein and Marie

 * Seriously, look at her and them
 * So, if she is Marie and Stein's daughter, could it be that Gavrill is actually Stein and MEDUSA's Daughter, only she's a Wolf Witch rather than a Snake Witch?! Brain Bleach is on...
 * Better yet, the professor IS Stein. My guess is out as to what age is currently is in the manga.

Dr. Black Jack gets her expertise from Prof. Madaraki.

 * ... Which in turn catches his antisocial behavior, disdain for the system, and other various eccentricities..

Fran is Illuminated
It's as good an explanation for her sense of right and wrong as any.
 * Who is an automaton constructed by Professor Madaraki, starting as a Beholden then catalyzed as a Hoffnung.

Fran does enough traditionally successful operations to cover for the...unappreciated ones.
Hence people constantly coming to her. However, these are not interesting enough to warrant stories.
 * Clearly true. Explicitly stated as true, in fact, in chapter 30. We even see a few that are well intentioned and don't backfire on the page, though the majority are...ill-thought-out, with a handful that are actually malevolent. Although a couple of the backfires don't backfire in a way the client would consider them backfires (the Sentinels, for instance).

Madaraki and Fran are the last known Sparks.
Since the two series are in two different time periods, one could presume that all the other Sparks killed each other over the time difference and Madaraki and Fran are the only known ones left. Really, compare the mad science between the two. Fran and Madaraki just focus more on medical sciences rather than death rays and such.

Fran is an Igorina.
Visible stitches? Check. Epic surgery skills? Check. Devotion to her Mad Scientist master (prof. Madaraki)? Check. She doesn't talk like The Igor, but many modern Igors don't.
 * Hell, Igorinas never lithped as much as their male counterparts, at least according to Monstrous Regiment.

The story takes place in the same universe as Mai-chan's Daily Life

 * Somewhere out there, Fran is just chillin', utterly unaware of the fact that one of the Professor's surgeries resulted in the Healing Factor of Mai and her brother... of course, if she does find out, she's gonna be pissed.

Fran made Tomie

 * She accidentally made one self-replicating girl (#13), then went on to make an army out of them (#44), so perhaps she decided to go one step further?
 * I always thought Franken Fran had some Junji Ito flavour to it.

At some point in his life, Professor Madaraki met and fell in love with Romana's second incarnation.

 * And so he designed Fran after her. Because I just can't unsee the similarities in their appearance.

Fran suffocated to death at the end of Chapter 61.

 * Simply put, the odds that that the cabin room still held enough oxygen within to keep her alive by the time Okita and Veronica got there is incredibly small. The reason for her dream is that she fell asleep due to lack of oxygen.

The Black Lotus doesn't actually plan to destroy the world by building orphanages, offering medicine, causing overpopulation, etc. They are actually just conventional supervillains.

 * The Black Lotus leader only claimed that this was their plan when cornered by Sentinel II. By doing this, he tricked Sentinel into becoming a terrorist and helping their cause. This would explain why he stopped his followers from attacking Sentinel. It would also explain why Black Lotus has to turn its members into monsters.