Time

Spiritron record anchoring band[1].
A Quantum Timelock is a metaphysical event, it calculates the average “value” of each parallel world’s events, then locks past events down. A phenomenon that separates what was, and is, from what might be.
Our universe allows for countless possibilities and creates many parallels worlds and histories with different developments.
The universe has a finite amount of energy to spend maintaining each parallel world. Because the universe itself would expire if these realities were to expand without limit, it conserves energy by, excising worlds, at specific intervals, that have veered too far from the strongest, most stable timelines.
The Moon Cell has concluded that the universe we perceive of, which should be unstable, is being stabilized across the present, past, and future by this culling process and by quantum time locks.
The easiest way to visualize the process is to envision time as a giant tree, one that would grow indefinitely if left alone. The excision process is comparable to trimming the unneeded branches and leaving only the trunk of that tree.
History that becomes a part of the “time lock”2 will not change, even if it is affected by the past and future. The incidents that occur during a time lock will, in fact, never change, no matter what happens.
Even if one were to go back in time before the time lock to try and change history, once one reached the time lock, history would be forcefully restored to what was already registered there.
In a universe with quantum time locks, the outcome that is registered in an quantum time lock will not change. A time traveler can only alter the “process” by which it happens, but never the “result.”
For example, imagine that there was a war in Britain, and that the “result” that was locked in afterwards was that Britain was destroyed.
Even if you could manage to travel back in time and affect history so that Britain flourished, the war ended peacefully, and everyone had a happy ending… the moment that history reached the time lock, it would cause whatever “corrections” were necessary to ensure that, despite your efforts, Britain was still destroyed.
You might be able to change the lives of one, two, or perhaps even a handful of people, but you could not change the course of the vast river of human history.
That is the “Quantum Time Lock,” also known as the “Foundation of Human Order” in the world of magecraft.
On the other hand, it could be possible to deny human history from its foundations by destroying a quantum time lock through some great feat. But even with that method the most that could be done is deny human history beyond the destroyed quantum time lock.
The ones who can determine the next coming quantum time lock are those living in the era. Past and future intervention cannot affect the quantum time lock.
Archimedes’ goal in this game is to completely destroy the Moon Cell before the next quantum time lock, leading to a base world that would start from that precondition.
While it is normally not something that could happen, to do that Archimedes continued to shift across worlds.
If Archimedes were to completely shut down the Moon Cell before the setting of the next quantum time lock from his subjective perspective, he would achieve victory.
Although Archimedes emerges victorious on several occasions, he is not able to destroy the Moon Cell in any timeline.
While Archimedes was endeavoring to bring his plans to fruition, the Main Character was able to prove proved the route of a world that was average yet with the most potential to grow, and the quantum time lock was decided.
And just like that, Archimedes’ plans went up in smoke.
By the way, the timeline where the Main Character entered the titan’s cavern with Archimedes and was split into several pieces (right after the start of the main story of EXTELLA) is listed as “Quantum Time Lock A,” while the True Nero route ending is “Quantum Time Lock B.”
No matter what Archimedes does within this timeframe, the final “result” has already been determined.

[1]In the book, the term is printed as 霊子記録固定帯, however in-game (both Extella and FGO) 量子記録固定帯 is used. It is likely that 霊子 (spiritron) instead of 量子 (quantum) in the context of quantum timelock is a typo.

Golden White Face [Circumstances]
Konjiki Hakumen.
This is the nine-tailed divine spirit form of Cas-ko. In this form she is a pseudo-god that is a deification of the sun. You get a peek of her like this in her 3rd Secret Garden. The apathetic Sun Goddess [Amaterasu Oomikami].
When Cas-ko goes into nine-tails mode this is what she will……not be. This form is Cas-ko’s origin, and is now just something that’s been part of her since long ago and continues to be a part of her. When she becomes this high level of a divine spirit, the time axis is no longer a limiting factor to her.
Normally someone entering the mausoleum would be burnt to a crisp, but as expected of our Zabio/Zabiko [nicknames for the male/female protagonist] he or she flaunts their recklessness in the face of danger (stupid menu choices), and somehow pull through.
Originally we wanted to feature her without clothing (in her lovely nine-tailed divine spirit form wearing only an apron [naked-apron]), however, unable to break through the ethical wall that is our consciences, she appears properly clad in her ceremonial attire.
By the way, when someone who has no dream enters the mausoleum, the only thing that can be seen is a giant sun.

Holy Grail [Circumstances]
This had once been a term pointing out to the "wish granting machine that could grant any wish", but in Extra it's referring to the "right to use the Moon Cell."
If you browse through the vast records of Earth simulations stored in the Moon Cell, you are sure to find the Earth with the future you desire.
All you, you who have earned the right to use the Moon Cell, have to do is tell it this:
"Recreate my ideal future."
The Moon Cell should quickly move things forward so that the Earth will take the shape of that future.
For the Moon knows how, it knows all that is to be done to make it so.

You might say “I want all the girlies in the world to be mah little sister" for example, and then in about ten years, it would be assumed that society on Earth would be reorganized in that fashion.
Or the Earth as a whole might be managed so that an apparatus that can make that dream “seem real” would be created.

There is nothing that humans can’t realize as long as it lies within the scope of human imagination.
Because whatever kind of illusion it is, however much of a pipe dream it is, there is a way to experience it.

Moon Cell’s core is Moon Cell.
As far as Moon Cell is concerned, the seven layers that make up the interior of the Moon are just “additional memory.”
Moon Cell’s core is what really manages the Moon and observes the Earth. It is the brain that stores the data about the past and future.
It observes the determination of every possible destiny every second, computes further results, and stores everything inside itself as light.1
There are untold tens of millions of lights years of light trapped within the core, and the entire photonic crystal structure is also powered by it.
A certain person named Moon Cell’s core, “The Destiny Perceiving Dendrogram.”
Just by using information encoded by converging light Moon Cell’s core can even rewrite the laws of physics.
Phenomena Selection Tree Angelica Cage.
◆
…The ability to enter Moon Cell’s core is the forbidden fruit that is offered to the ultimate victor of the Holy Grail War.
After overcoming the Seven Seas the protagonist, who is the last one left alive, finally makes it to Moon Cell’s core.
A sea of light and innumerable coffins await him/her there.
And there the one that waits for the protagonist, upon the rubble of the entombed remains of the many victors.
^ Stores as light means stores in the photonic crystal (think super advanced fiber optics).