Founding Titan

"Frieda's Titan stood at the apex of all others, in other words, a Titan that held an invincible power."

- Rod on holding the Coordinate.

The Zahyō (座標), named so by the people of the Hometown, is an ability that is capable of allowing the user to control the actions of the Titans, modify the memories of others in the majority bloodline of the walls, and inherit the memories of those who previously possessed the ability. It is passed on to successors by a ceremony in which the current holder is eaten by a human-turned-Titan. It is currently in the possession of Eren Yeager.

Description
This power is a composition of three different abilities.

First and most noticeable of all, the Coordinate grants the user the ability to control Titans at will and make them follow virtually any order. This is seen when Eren unintentionally commanded nearby Titans to eat the Smiling Titan and to attack the Armored Titan. It was also used by the First King to build the walls, making many Colossus Titans harden their bodies and confine themselves into the resulting structures. The real limit of this power is unknown, but as it can be observed, it extends to the point of making Titans perform actions that threaten their own lives. It was also mentioned by Rod Reiss that the power is so strong, it has the potential to wipe out all the Titans if the user is able to wield it to its full strength.

Secondly, the Coordinate allows the user to erase or modify the memory of a single person or even those of entire countries if they are skilled enough. It was used by Frieda Reiss to remove Historia's memories about her visits, and by the First King to make humanity forget all the history of the world before the building of the Walls, becoming the only holder of the Memory of the World. However, it is known that at least the Ackerman bloodline, the Asian clan, and the noble families are immune to this mental manipulation due to not sharing a common bloodline with the majority race within the walls. This caused the persecution of the former two at the hands of the Royal Government.

Thirdly, the power allows the user to inherit the memories of the previous holders of the Coordinate. This ability goes back to the memories of the First King in a time before the building of the walls, giving them omniscient-like knowledge about the world, including the reason the Titans exist and how the Walls were created. Nevertheless, it seems that only the Reiss bloodline can activate this ability from the beginning, since Uri and Frieda Reiss showed signs of being aware of that knowledge immediately after obtaining the Coordinate, while Eren was only able to see some vague memories of Frieda after years of having received it. The user is referred to as the living compendium of humanity because of this.

The overwhelming extent of these combined abilities causes the Coordinate to be referred to as the "invincible power", and the user to be called "God", as stated by Rod.

Despite inheriting the Memory of the World and the power to control the Titans, no holder of the Coordinate expressed any desire to resolve the Titan threat and free humanity after inheriting the power, even if they had expressed the desire to do so before receiving the power.This was because these holders of the Coordinate had inherited the ideology of the First King as well as his memories. Frieda used to suffer from fits of madness and depression due to those memories, and claimed that humans were sinners who deserved their punishment.

Like Titan Shifting, the Coordinate is apparently not inherited by bloodline, and the only way to get it is by eating the previous user. This is usually done by using a serum to transform into a Titan, then eating the holder and thus regaining human form, plus obtaining the Coordinate power and the Titan Shifting abilities. This means that all the Coordinate users have also been Titan Shifters.

The Coordinate originally belonged to the Reiss family, which passed it down generation to generation through the aforementioned process. However, seeing that they would never do something to stop the Titans despite having the capability, which allowed the invasion of Shiganshina and the death of his wife, Grisha Yeager stole the Coordinate by attacking the Reiss family in his Titan form and eating the former wielder, Frieda. He then transformed his son Eren into a Titan and allowed himself to be eaten by him, so that he could master the Coordinate without the memories and influence of the Reiss bloodline and accomplish the goal they never did.

Trivia

 * The Coordinate, as well as other Titan abilities, is retained in the user's spinal cord fluids, so it is not necessary to actually eat the whole wielder to obtain the power.
 * According to Rod, this power can only be used to its full potential by a descendant of the Reiss family, which is why Rod tried to have Historia eat Eren, due to the fact that she was the only remaining heir of the Reiss bloodline. However, the truth of this claim is unknown, as Rod was presumably luring Historia into simply killing Eren to reclaim the power.
 * Hange Zoë created the term "Progenitor Titan" (始祖の巨人) to refer to the Coordinate and any Titan Shifter who could master its power, including the First King.