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Exceptions are individuals who are capable of breaking the Game's loop. They are excluded from the Game early on to let the Game function as intended. They can be brought upon by two Sacred Artifacts with powers whose opposition fall outside of the System.
The contradiction between Sacred Artifacts is usually among Rules; however, generally, it can be caused by anything outside of the System involving Sacred Artifacts. Because the System can't decide which Sacred Artifact has priority, and so both Sacred Artifacts overflow with the power of their Rule. This overflow of power leads to the formation of an Exception. Since Exceptions form among two clashing artifacts, generally speaking two Exceptions are formed whenever Sacred Artifacts clashing fall outside of the System. A notable exception is clashing Sacred Artifacts with the Protagonist, who has not formed their own Exception despite bringing about the Exceptions Yog-Sothoth and the Witch of Orleans from the other clashing Sacred Artifact.
An Exception can be controlled in its power, as tested by the Berserkers. The Exception can be bound to an enclosed area set by a guild, so long as the instigators of the Exception remain within the area enclosed area as well. The Exceptions power can also be attenuated by maintaining a pre-existing hierarchy of the instigators within the guild, such as that of the Ranker system set up by the Berserkers.
Exceptions take the form of the Sacred Artifact's original owner, which is summoned but without their memories. These Exceptions are perhaps not be the actual original owners, but the product from the memories stored inside the Sacred Artifact. If the original owner is the current owner, then the current owner becomes an Exception, with the Sacred Artifact overflowing power seeping into the owner.
A list of Exceptions is below:
Establishing hierarchy between the current owners of the conflicting Sacred Artifact will terminate the Exception. According to Toji, the best way to accomplish hierarchy is through physical contact on places of the body significant to summoning. This can be either through lips (where summoning is vocalized) or on one's summoning emblem.
A hierarchy may be established through a third party. For example, Shiro had formed a guild with the Protagonist and Kengo, with the Protagonist as Guild Master, enabling Kengo and the Protagonist to form a hierarchy. The Protagonist also forms a pact with the Stray Transient Oniwaka, enabling them to form a hierarchy with him as well. Through this set up, the Protagonist was able to set the hierarchy of Kengo relative to Oniwaka to terminate an exception that these two instigated.
In computer programming, an exception refers to a condition in a running program that the system is not programmed to handle and thus, threatens its stability.