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Counter Magic (無系統魔法) is magic used to neutralise or obstruct the use of opposing magic. There are various forms, but most are categorized as Non-Systematic Magic.
- Mayumi used Psion Bullet against Mitsui Honoka, when she was trying to defuse the tense situation between 1st year Course 1 and Course 2 students.  Her conversation with Watanabe Mari hints what is the difference between this magic and Gram Demolition. 
Magic Dismantling or Gram Demolition is a magic that demolishes the record of Magic (Gram).
Gram Demolition uses compressed Psion particles to forcibly blow away all the accompanying Activation Sequence and Magic Sequences — anything that has traces of Psions recorded on it. The compressed Psions themselves travel through the physical realm as opposed to the Information Dimension.
Though it is called magic, it is simply a cannonball of Psions that has neither structure nor a Magic Ritual to modify an event, so it is not affected by Zone Interference (another form of counter magic). The pressure of the cannonball also repels the effects of Cast Jamming. It has no physical effects and cannot be hindered by any obstacle. Besides its short effective range, which is a side effect of the Psions traveling through physical space, Gram Demolition has no true weaknesses. However, because Gram Demolition is a compressed ball of Psions within the physical realm, an excessive Psion Count is needed to activate it and very few people can use it. Mayumi, a powerful magician in her own right, has said her Psion count is not enough to use Gram Demolition.
Other variations of "Gram Demolition" are Contact-Type Gram Demolition and Far Strike.
Contact-Type Gram Demolition
Contact-Type Gram Demolition is an alternate form of Gram Demolition used by Tomitsuka Hagane during the mock battles against Takuma and Tatsuya. Unlike the usual Gram Demolition which functions like a cannonball, Contact-type Gram Demolition works like an armor composed of formless Psions, demolishing any magic that comes in contact with the user's body. Contact-Type Gram Demolition cannot protect the user from the purely physical effects of an enemy's attacks and thus it is not a true "armor".
Far Strike is a form of Gram Demolition developed by Tatsuya. It works in the Information Dimension (Eidos) rather than the physical realm. Far Strike affects the astral form rather than the physical form, the "soul" to be specific which he can "see" with the aid of Miyuki (specifically when the target contains no physical body and hence cannot be seen by naked eyes).
Gram Dispersion or Magic Dissolution is one of the two strongest Counter Magics within Non-Systematic Magic. This magic takes a Magic Sequence and reduces it into a group of Psion particles without a meaningful structure. Due to the nature of an object accompanying a phenomenon, if the information has not been exposed, it is impossible to interfere with the magic. On the other hand, if the Magic Ritual is decomposed, the phenomenon will not occur.
To analyze the magic before the magic is activated in the present age where invocation takes a fraction of a second requires the ability to "see" and analyze the magic structure. Since the user is typically required to understand the magic being used beforehand, utilization of this magic is thought to be impossible. However, Tatsuya is able to use this because of his other ability, Elemental Sight.
- Main Article: Freeze Gram
Freeze Gram (術式凍結) is a counter magic which "freezes" the gram (Psion) in the middle of activation, thus it results in failure of target's magic activation due to incomplete magic ritual. In other words, it can only counter before magic invocation. Freeze Gram is more efficiently used against any Non-Systematic Magic.
Miyuki developed this counter magic with assistance from Tatsuya.
Zone Interference (領域干渉) is one of the common means of disabling the opponent's magic by using the user's own Magic Power to nullify opposing magic. By casting magic without a defined event-modification, it is anti-magic solely for the sake of disabling other magic. Since the magic has no target, the technique designates a fixed area with the caster at its center as the caster's "zone". This doesn't bring about a change in information, or Eidos, of anything within the zone, but instead creates a threshold for any spell or technique that seeks to change the Eidos within the zone to overcome in order to take effect. If the interference strength of any subsequent spell cast by the opponent is less than the interference strength of the initial caster, then the effects of the spell do not take place.
Zone Interference does not reverse magic, but rather directly prevents the opponents' magic in this manner. As such, existing phenomena will continue, but will not be sustained by magic. Zone Interference is indiscriminate in that it does not just apply to the opponent's magic, but applies to any magic of the caster's allies as well. Zone Interference works only on magic that seeks to alter the Eidos, so it is powerless against Non-Systematic magic.
- Related Article: Convergent Systematic Reinforcement
Data Fortification (情報強化) is another common way to counter magic.The caster replicates the Eidos, the records of the current status of an information body, and projects it back onto the target to protect the target's Eidos from being altered from that state dictated by the projected Eidos. This prevents magic from affecting the target.
Data Fortification, which focuses on single or few targets, is said to be much more efficient than Zone Interference.
Data Fortification has been stated to be used both passively and actively by Magicians on their own bodies to prevent themselves from being affected by an opponent's spell.
Cast Jamming is any Non-Systematic Magic that scatters the area of interest with vast amounts of meaningless Psion waves. The scattered Psion waves function as "noise" which disrupts meaningful Psion wave activity. This reduces the data upload speed of magicians in the affected area to their base station (CAD) by means of overwhelming it with large amounts of useless data. This in turn causes the Magical Rituals (Magical Sequences) the magicians use to be unable to affect Eidos. The Psion noise propagates in a random manner, and rapidly across all eight varieties (types) of the four Systematic magic frequencies. This results in them becoming what's essentially an antennae that blocks all forms of Psion transmission.
Cast Jamming is often performed using an Antinite material; because the user simply requires to do is generate Psion noise for their Cast Jamming to take effect, their strength in regards to their magical power is not important.
Pseudo Cast Jamming
Pseudo Cast Jamming is a Non-Systematic Magic that has been theoretically devised by Tatsuya, despite his claims to have discovered it by chance. It generates Psion noise without the use of Antinite, and accomplishes this by having multiple CADs simultaneously cast magic so that the Psion waves they emit interferes with one another. The interfering Psion waves act as noise, which modifies them all into a state of uselessness. This in turn results in the failure of using magic in the affected area in most cases. Leo has at one point referred to this magic as "Parallel Cast".
Failed magicians (experimented magicians), as well as STARS members are able to use this magic well. The effects of this magic can also be caused when multiple magicians cast magic at the same time (Such as during the suicide attack on 2095 Nine Schools Competition participants of First High School).
Specific Cast Jamming
Tatsuya uses an advanced version, i.e. Specific Cast Jamming, by initiating an interference magic activation sequence in one CAD and starting a reverse ritual in the other CAD, those 2 activation rituals amplify each other without translating into magic rituals. (Requires 2 CADs)
Tatsuya is able to use this technique with 1 CAD as well since he can read the activation sequences while they are being built and therefore cast a reverse ritual simultaneously. Since, even sustained type magic rituals, need to be recast, Tatsuya can use Specific Cast Jamming technique to stop its activation (reactivation).
Tatsuya is the only known user of this magic, and can use it due to his ability to read activation sequences as they are being constructed by CADs. Tatsuya first used this technique during his attempts to hide his abilities at the start of the series. Later, he relied more on Gram Demolition, the technique he revealed during the Nine Schools Competitions. During military combat, he uses any of the Cast Jamming methods within his arsenal.
One of the disadvantages of Cast Jamming is that, unlike Zone Interference, the user's own magic will also be affected even if the magician in question consciously tries to tune to the noise of Cast Jamming, as his subconscious mind will reject it. (Magic processing takes place in the subconsciousness, and thus the actions of the subconscious mind has priority over the conscious mind)
It is described as several piercing sounds, background noise from the Psions. It was used by the members of Blanche during the Incident in April.
Antinite is a stone capable of emitting Psion noise. Psion noise is essential for Cast Jamming. Antinite is a military resource and not something a civilian can obtain.
Within the world, there are supremacists who discriminate against magic, as well as extremists who condemn it. Yet since the production of Antinite is so small, they remain below the surface and are not a real threat.
Incident in April 2095
- Main Article: Enrollment Chapter (II)
During the terrorist incident in April 2095, members of Blanche along with the recruited members from Course 2 infiltrated First High School, and a few of them were wearing bracelets or rings containing Antinite, including Sayaka who used it to escape.
Cast Jammer is a cutting-edge technology developed by USNA, to distrub magic activation. This device has an appearance of a flashlight whose muzzle looked like a trumpet.
It produces "psion noise" which will leads to misbehavior of victims' CAD. Even though victims magic will not stop completely, their activation speed will be heavily affected and they need to pour excess psion in CAD in order to maintain or activate magic than in normal condition, which will drain magicians psion reserves much faster and cause heavy inconvenience in battle. 
- The First High School's curriculum moves from "Foundations of Magic" class and progresses to "Applications of Magic", starting from second semester of Second Year students. However, the concepts surrounding "Counter Magic" (magic that nullifies opposing magic) are taught during the first semester of Third Year.