Mystic Eyes of Death Perception

The Mystic Eyes of Death Perception (直死の魔眼) are an ability in the Nasuverse. Only two characters are known to possess them: Ryougi Shiki and Tohno Shiki

Description
The eyes are not really different set of eyes but are a circuit (possibly similar to a Magic Circuit) that opens up in the users brain and normal eyes, allowing them to "perceive death" in the form of lines and dots. The user in question is the only one who can touch or use these lines and dots (i.e. no one can interact with the lines/dots even if the user of the eyes were to point out their location on something). Beings that do not possess the concept of death are immune.

These lines can then be traced with a sharp object such as a knife or a sword. Cutting the line “breaks” the object along that line and damage inflicted this way can not be healed or repaired in any way. Healing is possible if cutting the line doesn't completely separate a part of the object from the object itself. Also of note is how Arcueid was cut into a multitude of individual pieces as a result of having her lines traced but was able to survive anyway despite not being able to regenerate. She was able to accomplish this by completely reinventing the inner structure of her body, abandoning the conceptual structure that had been traced.

Dots can be pierced by sharp objects. Piercing a dot effectively “erases” that object from existence, in a sense that the object loses even it's inherent properties such as momentum, toxicity, and generally any effect it may impose on it's surrounding. Living things whose dot was pierced get “stopped” and, as a consequence, die. While this death may not be instant, it is absolutely permanent, and can't be reversed or bypassed, even by reincarnation.

Note that Tohno Shiki shows signs of mental/physical strain when using this ability extensively, manifested as headaches and even temporary loss of sight. Arcueid noted that this is due him having to “connect” to the perspective of an object he wishes to see the death of and that perceiving thing in a way not meant for humans is putting a strain on his brain.

Acquiring the eyes
The only way to acquire the eyes is by having a near-death experience. It is possible it has do with the user in question getting close to Akasha (the route of all things) due to this experience. However, this ability is extremely rare, to the point of being thought of being no more than a myth.

Tohno Shiki acquired the eyes after nearly dying in a fight with his "brother". Shiki already had a form of jougan (magic eyes) from his genetic family, this may have helped him get the eyes. Shiki did not accept the eyes and later acquired Magangoroshi (魔眼殺し) glasses (made by Aozaki Touko and reinforced by Aozaki Aoko) that removed them from his sight.

Ryogi Shiki acquired the eyes after a two year coma. Her eyes are much more advanced than Tohno Shiki's allowing her to see lines on objects more distant from human perception without any notable strain.

Levels of Perception
So far, two levels of perception have been observed by various users:
 * Tohno/Nanaya Shiki: Possesses the ability to perceive the death of not merely life but the underlying existence of anything physical. In this case, the eyes can be used to annihilate the "existence" of the object. When applied to a living person's body, it doesn't directly "kill them" but rather "annihilates their existence" and because something that doesn't exist cannot live, the world will correct the contradiction and bring "death" to the nonexistent person. In this way, Tohno/Nanaya Shiki's eyes and Tohno Shiki (Roa)'s use of their eyes can be viewed as ultimately different: While Tohno Shiki (Roa) can only kill "life" and bring it "death," Tohno/Nanaya Shiki can kill the "existence," which, if applied to a living object, will consequently result in a "life" "dying."
 * Ryogi Shiki: Possesses the ability to to perceive the death of life force and also the death of the existence of objects and concepts alike. At this level, it enables her to perceive and annihilate physical material, persons, diseases, ghosts, intentions, and even magecraft.

While it hasn't been mentioned if Tohno/Nanaya Shiki can or not kill concepts (he has yet to be put in such a situation), it is specified that it is easier for Ryougi Shiki to kill immaterial things, while Tohno/Nanaya Shiki can kill material things easily due to how he feels no resistance.