Calculate Fortress

Calculate Fortress (演算型・衝撃拡散性複合素材 (カリキュレイト＝フォートレス) ) is the mysterious material that the Windowless Building is composed of, and is said to be able to withstand all impacts and is said to be stronger than air-raid shelter.

Principles
Calculate Fortress works not because it is hard, but because it uses electromangnetic waves or ultraviolet rays to calculate the pattern of the approaching shockwave, and then the mobile armor plates carry out the optimum vibrations into cancel out the approaching shockwave. It also has countermeasures against all types of chemicals and high or low temperatures. The Calculate Fortress only feels like a thick rubber panel to the touch, due to the offsetting waves running through it in order for it to distribute and let shockwaves escape, but the true composition of material is unknown.

It is apparently strong enough to protect the building from a nuclear strike and remain unscathed, and is able to withstand, without a scratch, an attack from a concrete wall-turned projectile that Accelerator threw at it using five minutes worth of earth's rotational momentum (an entire building in the anime). This attack slowed down the planet's spin by five minutes. Despite the power of the latter, Aleister Crowley could barely feel the attack, and the vibrations didn't even shake the liquid that he was floating in.

Weaknesses
However, the Calculate Fortress is not all that strong in and of itself, as when the intellectual portions fail to activate, a direct explosion is enough to blow a hole in it. As such, as unlikely as it is, if the Windowless Building runs out of power, Calculate Fortress is rendered useless. Moreover, the machine has idiosyncrasies when cancelling out shockwaves, as such there are some shockwaves that the armor cannot fully escape. If ever a competent person can calculate the shockwave pattern, then they can open a hole in the Windowless Building. Using this technique requires the usage of advanced computers to calculate and predict the impact patterns.

Deep Blood Arc
Calculate Fortress is first referenced during the introduction of the Windowless Building and Aleister Crowley. However, its full capabilities are not explained, and is only referred to as something that can withstand all impacts, and making the Windowless Building as stronger than an air-raid shelter.

Ichihanaran Festival Arc
The main objective of Kamijou Touma and Thor is to break Fräulein Kreutune from the Windowless Building. Despite having the feat of withstanding even Accelerator's geo-rotational momentum powered-attack, Touma and Thor manage to crack the Calculate Fortress using a jackhammers after calculating the weaknesses of the Calculate Fortresses' impact diffusing abilities, and is later broken completely by Fräulein Kreutune.

Aleister Crowley Arc
In their attempt to help Touma who was facing Aleister within the Windowless Building, Misaka Mikoto and Shokuhou Misaki cooperated in order to breach the building. With Misaki's assistance and the Anti-Art Attachment, Mikoto managed to break through the Calculate Fortress's defenses and penetrate the building using the Liquid Proof Railgun.

Trivia

 * The Calculate Fortress was referenced in passing in Toaru Majutsu no Index Light Novel Volume 02 and took 27 light novel volumes from the main series, including both SS novels to be reintroduced.