Urban Legend

Urban Legends (都市伝説) are a form of modern folklore consisting of stories that may or may not have been believed by their tellers to be true. As with all folklore and mythology, the designation suggests nothing about the story's veracity, but merely that it is in circulation, exhibits variation over time, and carries some significance that motivates the community in preserving and propagating it.

Urban legends are a unique part of the world of Toaru Majutsu no Index, specifically Academy City. The legends and rumors are quite often important to the plot later on, and in Toaru Kagaku no Railgun is a central point in several storylines, having many storylines based on an urban legend.

In the Toaru Majutsu no Index universe
Despite being the city of science, urban legends are still quite pervasive in Academy City, apparently having entire websites dedicated to following and recording details on urban legends. Because of the fact that they are in Academy City, the rumors and legends take a pseudo-scientific appearance, having basis in the Academy City.

They are first defined by Tsukuyomi Komoe as nothing but rumor talk related to the unknown "Seven Mysteries" that are supposed to be around Academy City. This is of course ironic since Komoe Sensei is herself considered one of the seven wonders.

Evolution
Despite the many ridiculous and ludicrous situations that are featured in rumors and urban legends that a person may somehow run into and not escape. Urban legends and rumors are constantly "looked into" or change to accommodate weaknesses in order for the person that may run into one of the situations in urban legends and rumors to escape. And even then, such things continue to evolve to even more complicated rituals or change weaknesses or strengths regarding the contents of the rumors and urban legends.

For example, if a rumor was spreading that said no one could escape from a certain woman who could run 100 meters in 3 seconds, a different rumor would be created saying one would be safe as long as one had some hard candy or pomade. Then another rumor would crop up saying the hard candy and pomade only worked on the original woman, but they were completely ineffectual against the second one whose mouth had been split open by the original woman.

The urban legends and rumors of Academy City is apparently a never ending cycle of changing its contents, to weaken or strengthen it. It is unknown if a rumor or urban legend is proved or disproved, though one can assume that actual information regarding the rumor will eventually replace false information of the rumor.

Imaginary Number District Rumors
Rumors about the Imaginary Number District are pervasive in Academy City, with several rumors popping up declaring that it is the first First Research Organization, it has Imaginary Technology, and that it secretly controls Academy City behind the shadows.