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.

This is how the concept of parallel worlds operates in the Fate/EX series.
It’s easy to understand if you think of Compiled Events as the “main route,” and Pruned Events as the “bad end” route.
However, Pruned Events are merely worlds where many possibilities have been lost due to excessive specialization and drifting too far from the main route, so they are not necessarily bad or evil routes.
If you were to divide these flows in terms of good and evil, a good flow would be a flow that is stable and most ripe with the possibility to give birth to other branches in the future,” while a bad flow is “a single flow that has become too radical and has no chance of changing its course because it has become a one-way street with nowhere else to go.”
There have been Pruned Events that have progressed further than any world within the Compiled Events, including utopian worlds that were filled with hope and happiness. However, since those outcomes are “complete in and of themselves” or “finished,” there is no need to see them through to the end, and so they are “trimmed” at the stage where the requirements for a utopian world are met.
The universe will not expend energy to create an ending where it already knows what will happen. This is because the universe continues to expand towards a “future” that no one has seen before, that not even a life form of a higher order could predict.

To give an example using the fighting game Melty Blood, the TATARI route is the Compiled Event, while the Tohno household supreme Kohaku route is a Pruned Event, but I digress.

Untranslated

A ghost that already turned into a phenomenon.
The fragment of a messiah that hates, endorses conflict.

"This future is mistaken… someone has to start it over."

The ghost drew such a conclusion about the thesis of EXTRA as a whole - "confrontation against stagnation".
This is a fight against stagnation, the evil nature of humans.
Will you advance while shedding blood?
Will you advance while taking someone's hand?
After despair, will you reject (travel all over) this?
After despair, will you affirm (settle) this?
The ghost inquires about such right and wrong.
As a responsible party born in the past, reflected in the present.

"The world has entered in a impasse.
This future has already approached a dead end. Humanity is unsightly ending halfway without bearing fruit."

Humanity has already ended.
This "stagnation" itself is proof.
Rin thought that this came from the rule of Western Europe Plutocrats.
That Leo and the others were suppressing the progress of technology, the undulation of emotions to their own convenience.
Leo too had such self-awareness. That the Plutocrats are controlling the world in this manner.
Howerver… Leo never told Rin until the end.
The Western Europe Plutocrats has made arrangements so that society would stagnate, but other than that no definite choice has been produced so far.

"The halt of the world occurred because you people desired so."

Nobody wishes, has any interest in the future and the likes.
Rather than going forward, it is much more comfortable to stand still.

To begin with… humans are enough happy as it is.
More progress than this, for sure that is something unnecessary - the consciousness of people say so.

"How absurd. Then there is no meaning to this. If it was just about wishing for happiness, it would have been better to remain as animals from the beginning. You people - we all - have shed much blood while seeking for something greater than happiness."

The ghost resents that weakness.
Why are people so weak, when they are that much strong?
Such ending, is it really worth 2,000 years?

"Humans that have forgotten conflict will just disappear. Struggle for existence is indeed the basis of life. The means to survive, in the true sense of the word."

Yes. Conflict is indeed the path of progress.
Kill. Open a path (Spread). Steal. Flourish.
If you kill this planet, then leave this planet behind and reach the cosmos (sky).
That is the bare minimum responsibility of humans.

"And, you yourself are its crystallization.
Contemplate that growth. Conflict nurtured you. Predicament changed that flesh and blood into steel. It let you surpass even first-rate hackers. Yet… you, who knows its preciousness, will reject this strife (wish)?"

　　　　　　　　　　　　　　◆

Moon Cell Nucleus
Before the eye of the moon, two ghosts confront each other.
They are both humans from the past.
Two of the few people that can express objective impressions about this future.
The king of conflict rejects this future.
However, you do not hold such point of view.

"Even without finding any value in this era.
Even if this future is all somebody else's problem.
Even if the time ahead that we dreamed about is a foolish dead end. I cannot reject the life of the people that live here."
"You approve this future?"
"No, I'm just like you. I cannot approve it.
…however, I still cannot bring myself to hate it either."

The observation mechanism that became the stage for the Holy Grail War.
The reason why its virtual world has the image of a sea.
If the basis of life is conflict, then the basis of the eye of the moon is to watch over.
That way of being was unconsciously understood by the Masters who arrived at the moon.
But only he, who managed to reach the Nucleus faster than anyone else, did not understand the strength of that way of being.

"…even so. Stagnation (this place) is our reality."

Tragedies that occurred cannot be changed.
The responsibility for stealing must be fulfilled.
While accepting the premonition of defeat, the fragment of a messiah takes up his sword without yielding his pet theory.

"Thinking back, mankind has already expired its adolescence.
Until the 1900, it was the growing period.
But, after experiencing the adolescence--- the immature era meant to follow it, the golden age that was finally supposed appear was practically non-existent.
Like a decomposed fruit.
The most rich and prosperous period was entirely missing.
That, was too much sinful.
If we don't leave behind an outcome enough to recompense the lost things, the fostered costs, everything will turn into lies.
This future is mistaken. Mankind has to start things over again. Small disputes are no good. Without a struggle for existence that turns all into related parties, our eyes, our consciousness will not grow."

Humans are more amazing than that.
Life, mankind must go to a place that even the humans of the past cannot imagine.
Such ideology of the innate goodness of man has pushed up this ghost to the level of a messiah.
Although his views are elitism-like, they are also correct.
Indeed, the humans of this era are worn out.
They are losing interest. They are giving up. They have long forgotten, what is to dream about the future.
But---

"To choose that is responsibility of the people who live in that era.
Twice H. Pieceman.
The era which you were supposed to protect, has passed away long ago."

The curtains of the battle rise together with the words of parting.
The final battle that overcame the seven seas.
Those who knows its ending, are only the Moon Cell and the player.