Transcending the physical realm where most of the story of Attack on Titan takes place, the Paths are channels or links between all Subjects of Ymir, bound through the power of the Founding Titan. The idea first emerged on noting that the Power of the Nine Titans randomly resurfaced in newborn Eldian children, if the previous holder of a Titan was killed without passing on their ability. This heavily implied that all Subjects of Ymir were connected through invisible bonds that exist beyond the confines of space and time. First appearing when Ymir, the previous holder of the Jaw Titan before Porco Galliard, ate the latter's brother Marcel when in her Pure Titan state. On regaining her consciousness and sense of self, she was transported to an unknown land blanketed in white soil that stretched endlessly in all directions, with dazzling auroras lighting up the sky.
In essence, these auroras are the visual manifestation of the paths in this world. While otherwise invisible to the human eye, the paths are mainly used to transport the flesh and bones constituting a Titan to the respective Titan shifter in need of them. They can also be used to help shifters regenerate or alter the memories and biological makeup of the Subjects of Ymir via the Founding Titan. One instance of this in Attack on Titan was in the erasure of the memories of the Eldians of Paradis by King Karl Fritz, after their migration to the island. The paths all converge at a glowing tree-like structure that represents the Founding Titan, termed the "Coordinate."
Emerging From The Coordinate
After her demise, Ymir Fritz, the mother of all Titans, found herself transported to the world of the paths, where she encountered the newly formed Coordinate. At this time, there were only three paths, corresponding to Ymir's daughters: Maria, Rose, and Sheena. Over time, as her daughters bore children and passed on the Power of Titans, the paths split further to encompass all the Nine Titans, as well as the Eldian race as a whole. Within this world, Ymir took on the form of her younger self and obtained a pail of water, which, she used in conjunction with the endless soil available to mold the bodies of Titans and heal injured Titan shifters as and when required.
It is only after being transported to this realm that Eren and Zeke realize the true nature of Titan transformations and the Power of the Titans as a whole. Besides transferring bone and flesh, the paths can also be used to transfer memories. This allows Titan shifters to access the recollections of their predecessors, gaining information or battle experience. Furthermore, this also proves to be true in the case of the Ackerman clan, who are able to gain the combat skills and experiences of their ancestors after "awakening." Hence, they are able to become seasoned veterans capable of manifesting near-superhuman strength in next to no time. Finally, the paths also seem to transcend time itself through the Attack Titan, as Eren Kruger had access to memories of Mikasa Ackerman and Armin Arlert before they were even born, since its holders were able to view the memories of their successors in the future. Eren was also able to summon all Eldians to the world of the paths through the Founding Titan in order to declare his intentions behind the Rumbling, signaling that this ability was only possible due to the paths' ability to link all Eldians across boundaries of space or time.
The World Of The Paths
A realm where time and space seem to expand infinitely towards the horizon, the world of the paths is a dimensional plane accessed by users of the Founding Titan, as per Zeke Yeager's speculations. Those transported to this place can experience an eternity pass by in a matter of seconds when compared to the real world. Zeke himself witnessed this first hand when he grabbed Eren's severed head, spending an immeasurable amount of time in the world of the paths as Ymir rebuilt his body. During this period, he was able to undo Karl Fritz's vow of renouncing war that had prevented previous Founding Titans from triggering the Rumbling to safeguard Paradis from the animosity of the rest of the world.
Inside the world of the paths, the Coordinate took on a corporeal form as a massive pillar of light that branches like a tree, which according to Tom Ksaver — Zeke's predecessor as the Beast Titan — highlighted how all Subjects of Ymir are a part of the Founding Titan. Eren Yeager entered the world of the paths when his severed head was caught by his half-brother Zeke — a titan shifter with royal blood — an act that activated his dormant Founding Titan abilities. While there, he found the youthful figure of Ymir Fritz, condemned to forever sculpt the bodies of Titans for all time. From this, it could be surmised that Ymir herself is the cause of all Titan transformations. Eren and Zeke also concluded that Ymir had no real free will of her own, and was bound to obey the commands of generations of Fritz royal family members.
An Eternity Of Servitude
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Eren's entry into the world of the paths provided Ymir with an avenue for escape from her desolate fate. On halting her from fulfilling Zeke's wish to prevent Subjects of Ymir from reproducing, he offered her a choice between the former's plan and his own, which involved the widespread decimation of the global population with the aid of the innumerable Wall Titans on Paradis. When finally given a chance to gain her own freedom, Ymir chose to give up her power to Eren, allowing him to release the Colossal Titans inside the Walls. Eren speculated that Ymir had been waiting centuries for someone to come and release her from her never-ending ordeal, and it was his recognition of her plight that convinced her to give him the power he needed to rid the world of Titans once and for all.