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Misaka Mikoto seems to know about the sisters before the Sister's-arc, as she
says both in the prologue of the first LN and the Railgun-manga:

> Have you heard how my DNA map was supposedly analyzed and military Sisters
> were created based on it?

How did Mikoto know about the Sisters back then? She found out during the
Sisters Arc (which happened later) that the Sisters exist and the rumor just
spread then, too (at least it seems to me). How could she tell Touma about
them?


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a-certain-scientific-railgun
How does Mikoto know about the Sisters before the Sister's Arc?


Railgun S starts shortly before Index and continues through the different arcs
just from Misaka's point of view. Railgun however is the prelude to Index and
most of it takes place way before Index. Later on it catches up and things
start happening at similar moments in time. Because both Railgun and Railgun S
happen at similar points in time and move at a similar pace in stands to
reason that they are happening at the same time. Events will happen in
Railgun, than the sister's arc in Railgun S, and than back to some of the
other events in Railgun and so on and so forth.


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After Mikoto meets Nunotaba Shinobu, she [starts
investigating](http://toarumajutsunoindex.wikia.com/wiki/Sisters_Arc#The_First_Production_Plan)
her and finds her connection with the 7th Medical Research Center, who were
researching her DNA map to create an army of level 5 clones.

This is covered in the _Railgun_ manga and _Railgun S_ anime.

Initially she thought the Sisters project was abandoned because the clones
would only be Level 3 (thus not realizing the plan for an army of Level 5
clones), but it's not until later that she realizes the Sisters were utilized
for the Level 6 Shift project.


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The quote you have provided comes from the first of the light novels, which
take place on July 19.

> It was July 19th. The fault lay in that date. Because summer vacation would
> start the next day...

The Railgun version of the Sisters arc extends from August 10 to August 22,
according to the
[wiki](http://toarumajutsunoindex.wikia.com/wiki/Story_Timeline#August_10).

So Misaka had heard rumours about the Sisters for weeks, at least, before
coming face-to-face with one.

The full version of your quote goes:

> “Hah. Don’t make me laugh. What is all this about the ‘brain of god’? Have
> you heard about the supposed military Sisters created based on an analysis
> of my DNA map? It seems to me these lucrative side effects are more
> important than that objective.”

If you read the Railgun manga version of that encounter, you will see that
Misaka has an expression on her face like 'Really? People actually believe
that?'

Given how distressed she was when she found out the Sisters were real, I think
it is safe to assume this was a rumour that she heard but dismissed as
ridiculous.

Considering that the Sisters had been operating outside for some time, it is
hardly inconceivable that rumours of their existence had sprouted.

EDIT: Rereading the third novel led me to this quote:

> However, recently there had been a rumor spreading throughout Academy City
> that her DNA map had been used to create military Sisters. It wasn’t that
> rare an occurrence. Mikoto was one of the seven Level 5s and a scholarship
> student at the prestigious powers development school of Tokiwadai Middle
> School. There had been countless baseless rumors like that about her. That
> was why she had not believed the rumor.
>
> Or perhaps she had simply not wanted to believe it.


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