Founding Titan

"Frieda's Titan was the greatest of all the Titans. It possessed 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 Yeager 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. Over a thousand years earlier, this same ability was used by Ymir Fritz, the first holder of the Coordinate and the first of all Titans, to use the Titans to accomplish great deeds for her subjects, the forefathers of the nation of Eldia. 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 of 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 memories of the world. However, it is known that the minority bloodlines of the walls such as 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. Throughout the many centuries before the raising of the walls, this ability was used by the Fritz family, the ancestors of the Reiss family, to maintain order in the nation of Eldia while the eight factions of the Titan Shifters warred against each other.

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, and perhaps as far back as Ymir Fritz herself, 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 Reiss. It has been said that only a member of the Reiss family, and by extension the ancient Fritz family, can make full use the Coordinate. However, it appears that if the Coordinate is held within someone outside of the royal family, the power can still be used if the holder is in physical contact with a member of the royal family. This has been seen when Eren unleashed the Coordinate after striking the hand of Dina Fritz's Titan form, and some time later when Rod and Historia Reiss laid hands on Eren's back, triggering the resurfacing of Grisha Yeager's memories.

Despite inheriting the memories 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 Fritz family in ancient times, the ancestors of 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: to return the nation of Eldia to its former glory.

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.
 * 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.
 * The only known characters that would inherit the ideology and memories of the First King would be Zeke Yeager as the last Fritz, and Historia Reiss as the last member of the Fritz's Reiss line. It's unknown if Zeke has any children.