Avalon Scaling Fix

[LephyrTheRevanchist]

Again, I don’t see how this helps your point.
This could easily be parsed as C.C.C being an extremely versatile printer….which is what it does.

Because that's literally what I argued. It's not a literal 3-D printer; it acts as (synonym of like, btw) one by taking the fundamental stuff making-up reality and rebuilding it. It has nothing to do with dimensions, as in directions.

Imaginary Number Space is not tied to directions as far as I could tell, but possibilities and information, and they are abstract, since BB can influence abstract things with this ability.

 

[Agnaa]

Also, I’m pretty sure lower temporal dimensions cannot affect dimensions higher than them.

Also, we accept temporal dimensions on the wiki to have infinite snapshots of lower ones.... not higher ones, lol

No, you're wrong about how dimensions work.

Any "Nth dimension" framing is illusory. There is no objective metric by which you can determine the "order" of dimensions, and so, any statements about that sort of thing are irrelevant, except in that they tell us that there's at least that many dimensions. For an analogy, the same sort of thing is true for amount of a liquid. It wouldn't really make sense to say that a jug's fourth cup is oil, but hearing that you could intuit that there's at least three cups of something else (such as water).

So we don't have any requirements about temporal dimensions "affecting lower/higher dimensions" in different ways, since dimensions aren't ordered.

 

[Wankbreaker]

No, you're wrong about how dimensions work.

Any "Nth dimension" framing is illusory. There is no objective metric by which you can determine the "order" of dimensions, and so, any statements about that sort of thing are irrelevant, except in that they tell us that there's at least that many dimensions. For an analogy, the same sort of thing is true for amount of a liquid. It wouldn't really make sense to say that a jug's fourth cup is oil, but hearing that you could intuit that there's at least three cups of something else (such as water).

So we don't have any requirements about temporal dimensions "affecting lower/higher dimensions" in different ways, since dimensions aren't ordered.

Alright, but in this case there is a clear cut off here.
The planet (which is 6D) and the Throne of Heroes (which is somewhere below this), are noted to be seperate and freed from this temporal dimension due to their superiority, and not affected by the parallel world/pruning system

 

[Wankbreaker]

Because that's literally what I argued. It's not a literal 3-D printer; it acts as (synonym of like, btw) one by taking the fundamental stuff making-up reality and rebuilding it. It has nothing to do with dimensions, as in directions.

In the Jisho entry you linked, it says as as in “the role of”

Using the example sentence:

As a politician,he makes utmost use of his acting ability.

He is not metaphorically playing the role of a politician, he is one.

Imaginary Number Space is not tied to directions as far as I could tell, but possibilities and information, and they are abstract, since BB can influence abstract things with this ability.

Chaldea moves through it like space with the Zero Sail, and in the OP, I brought up a scan which calls it a “sea of time”.

Imaginary number space is not a directionless/dimensionless plane. It is explicitly given the description of a fourth dimensional plane multiple times,actually.

There are physical spaces that can be hosted in imaginary space itself.

 

[Wankbreaker]

as a side note, i will point this out once again.

Arcueid EXISTING in the mooncell in a super weakened state created a huge amount of stress on it and it’s systems.

Same Arc says that nothing in existence is able to destroy the 6D planet. (Which would also include her full powered self, which blows fate extra out of the water.) Her authority even in extra is greater than BB’s as her debuff authority works on BB, and even Amaterasu, who is noted to be the strongest character in extra.

It is thus illogical to assume that anything in extra has 6D or above power.

snip

 

[Violatas]

Think it'd be best to focus on the fact no one should scale to Avalon like what was proposed in the OP before this goes on too long

 

[Vietthai96]

I'm neutral on not scaling to Avalon point. But Throne of Heroes lower than Planet, wut??

 

[Wankbreaker]

I'm neutral on not scaling to Avalon point. But Throne of Heroes lower than Planet, wut??

It’s stated multiple times (including in the FGO prologue chapter), that the planet is the one that created it. I’ll edit this post with the scan in >10 minutes

 

[Wankbreaker]

Olga Marie Whether or not a hero truly existed, he or she is still "information that was produced on Earth," right?
Olga Marie To summon a Heroic Spirit is to convert the information stored on this planet into something for the good of mankind.
Olga Marie There are seven classes of Servants, which vary depending on a Servant's legends and abilities.
Olga Marie It's incredibly difficult to copy a Heroic Spirit entirely.
Human mages do not have enough resources or memory to achieve such feat.
Olga Marie That's why only one aspect of a Heroic Spirit is fixed in our world, resulting in the seven classes
Olga Marie Saber, Lancer, Archer, Rider, Caster, Berserker, Assassin.

 

[Vietthai96]

Olga Marie Whether or not a hero truly existed, he or she is still "information that was produced on Earth," right?
Olga Marie To summon a Heroic Spirit is to convert the information stored on this planet into something for the good of mankind.
Olga Marie There are seven classes of Servants, which vary depending on a Servant's legends and abilities.
Olga Marie It's incredibly difficult to copy a Heroic Spirit entirely.
Human mages do not have enough resources or memory to achieve such feat.
Olga Marie That's why only one aspect of a Heroic Spirit is fixed in our world, resulting in the seven classes
Olga Marie Saber, Lancer, Archer, Rider, Caster, Berserker, Assassin.

Since i don't play FGO, you can correct me, but this conversation, at least to me is ambiguous, kinda she just talking about convert existing information on Earth, because iirc, isn't Chaldea use different system compare to the actual Holy Grail Summoning system?

 

[Wankbreaker]

Since i don't play FGO, you can correct me, but this conversation, at least to me is ambiguous, kinda she just talking about convert existing information on Earth, because iirc, isn't Chaldea use different system compare to the actual Holy Grail Summoning system?

pretty sure Olga was talking about the grail system here, as they were in the Fuyuki singularity but it doesn’t exactly matter, as she is describing the process of summoning a HS in general. The information is produced, and stored inside the planet.

If you check the OP, there’s also a couple of scans proving this further.

 

[Wankbreaker]

He is describing time as a direction, stating it as the 4th dimension. This isn't a contradiction for there being more dimensions.

you want a contradiction, ill grant you one

"For example, take the Sister who somehow got mixed up with the Burial Agency. She says that through the Sabbath, she became demonized and gained higher-dimensional senses, becoming functionally almighty in this dimension. However, even she is still bound by matter. Still bound to this universe. If you ask why,

'I managed to save sentient beings and ascend to the seat of the Demon Heaven, but there I'm nothing more than a novice speck of dust.

I spent a lifetime gaining the eye of insight, only to find that what it saw was not just the truth of the world, but also a more miniscule version of myself. It's as if I strived only to know my own pitiful self; what was the point of this transformation? So, I remain here. No matter how minuscule this world may be, the me here has at least somewhat more value than the me over there---'

It's a foolish story. Because she became able to perceive the outside of this world, she became even more acutely aware of her own powerlessness. This is an example of the limitations of the individual."
「たとえば埋葬機関にいつのまにか混ざっていたシスターですね。彼女はサバトによって悪魔化し、高次元の感覚を得た事でこの次元では全能になったと言います。ですが、そんな彼女ですらまだ物質に縛られている。この宇宙に縛られている。なぜかと問いただせば、」


“あわよく衆生を救い魔天の座に昇りましたが、あちらでは<私|ワタクシ>など駆け出しの<塵芥|ちりあくた>


生涯をかけて観の目を得てみたものの、その目が見たものは世界の真理だけでなく、より矮小な私でした。
これでは惨めな自分を知る為に努力したようなもの、何の為の<変生|へんじょう>でしょう。
ですので、私はこちらに留まっているのです。
たとえどれほど狭い世界であっても、こちらの私は向こうの私より、幾分はましな価値がありましょう―――”


「愚かな話です。外を知覚できるようになったが故に、更に己の無力さを痛感してしまった。個人の限界を表した一例ですね。

Even though the text says she is still bound to the universe , that is purely by choice, as her higher dimensional senses allowed her to perceive the outside, and what lies beyond the world. Kiara wants to stay in the universe,as she feels as if she is too miniscule to whatever lies beyond.



This effectively means that the world is restricted to these 4 dimensions, as mentioned. If quite literally each and every one of the sparse pieces of information we get on these types of higher dimensions essentially say the same thing, it is no longer the exception,but a status quo.

 

[Vietthai96]

Still trying to find Throne stuffs but

She gained higher dimensional sense, not that her entire existence turn into something else. It is the same as you making a statement: Goku achieved higher dimensional power, but he still bound by the universe, bound by matter (which in fact he is)

This is just another way saying time is insanely crazy in the verse that it bound everything in it, not somehow the verse (or any other verses) can't have more spatial dimensions

 

[Wankbreaker]

Still trying to find Throne stuffs but

She gained higher dimensional sense, not that her entire existence turn into something else.

No matter how minuscule this world may be, the me here has at least somewhat more value than the me over there---'

It is the same as you making a statement: Goku achieved higher dimensional power, but he still bound by the universe, bound by matter (which in fact he is)

This is just another way saying time is insanely crazy in the verse that it bound everything in it, not somehow the verse (or any other verses) can't have more spatial dimensions

It is explicitly said that Kiara viewed the outside of the world/universe, and ascended to some different realm. Then she returned to this one. There is some form of dimensional cut off here.

 

[Vietthai96]

Fate Extra things again lol, but isn't it is stated she only gained higher-dimensional sense which allow her to see thing from higher dimensional perspective, but herself isn't higher dimensional. I checked Kiara profile but look like her HDE come from scale to True Demon and Saver, probably because the statement said she demonized, ahhh, damn, this is brainstorming

 

[Wankbreaker]

Fate Extra things again lol, but isn't it is stated she only gained higher-dimensional sense which allow her to see thing from higher dimensional perspective, but herself isn't higher dimensional. I checked Kiara profile but look like her HDE come from scale to True Demon and Saver, probably because the statement said she demonized, ahhh, damn, this is brainstorming

Whether it is just her perception or not is irrelevant really, just that her higher-dimensional perception allows her to see outside of the universe.

Kiara also did not complete her transformation into a true demon in extra, unlike in Tsukihime.

 

[Wankbreaker]

No, you're wrong about how dimensions work.

Any "Nth dimension" framing is illusory. There is no objective metric by which you can determine the "order" of dimensions, and so, any statements about that sort of thing are irrelevant, except in that they tell us that there's at least that many dimensions. For an analogy, the same sort of thing is true for amount of a liquid. It wouldn't really make sense to say that a jug's fourth cup is oil, but hearing that you could intuit that there's at least three cups of something else (such as water).

So we don't have any requirements about temporal dimensions "affecting lower/higher dimensions" in different ways, since dimensions aren't ordered.

Would the mooncell being called a Klein Cube be decent evidence for it being 4D?A Klein bottle is a 4D object, and im assuming nasu uses “Klein Cube” to essentially say it’s that in cube form.

there’s also this whole thing.

It is simply there.

A type-writer left behind by god.

An observation lens bored in the moon.

Later, the crystal ball of dreams would come to be called this.

An eye of the moon.

A bottomless Klein cube.

So we have:

BB’s strongest attack gained as a result of fusing with the mooncell have its strength directly derived from imaginary number space, which is 4D

The path to the core can be cut open by manipulating INS, as shown with Hakuno and BB

The Moon Cell being directly called a “Klein Cube”.

like the funny saying goes:

If it looks like a duck, swims like a duck, and quacks like a duck, then it probably is a duck.

 

[Expectro2000xxx]

I may be wrong since this is advanced mathematics but I think the Klein cube principle can actually be used for any R^X beyond R^4, similar to the Klein bottle that Felix Klein also invented, so that doesn't really seem to limit it to only 4D, feel free to ask someone more knowledgeable in dimensional math like Ultima or DT though.

Will say at least that something that probably supports it not being limited only to 4D is the fact that Kiara is described as more complex than a 4D cube, which along with the 8D statement should indicate that the Moon Cell isn't really limited to only 4D.

Scaling-wise, it would also make sense if the Moon Cell wasn't limited to 4D only since it could apparently replicate Avalon (the sheath is in Artoria room) and recently demonstrated the ability to just straight-up pierce through the anti-purge defense granted of Avalon.

Void Record: Moon Anchor (Write down the records, moon casket with no reader)

Rank: EX Type: Anti-Unit Noble Phantasm
Range: 10-50 Max. Targets: 1
The Human Order Foundations… Those are timelocked stretches serving as the cornerstone of human history. Absolute records that can’t be influenced by revisions to the past and future. On the moon, the Human Order Foundations are called Quantum Timelocks. This Noble Phantasm takes the anchor that locks them in place and uses it offensively. An Event Weapon that employs Imaginary Space to open the Mooncell Automaton's window, and fires the energy used for record-locking on a target. Not even the best defensive barriers (including Anti-Purge Defense) can negate this. However, it can be evaded by leaving its effect range. A rare situation where dodging is better than invincibility.

In regards to the Arcueid statement, I don't think it really contradicts stuff since we know that nothing from Earth can destroy Earth due to the defensive systems in place that prevent even things with the necessary strength from being able to do it, this is the entire reason of why Earth goes out of its way to fight aliens, as these defensive systems don't apply to them, hence why Excalibur had to be created in the Inner Sea (Avalon) and universe's furnace to make it the strongest possible weapon, and from Lostbelt 7 we know that even a full power Excalibur used against an alien threat can't kill or significantly hurt ORT (and as result Earth was destroyed because of its strongest weapon being useless).

And maybe it's just me but I don't see how the Tsukihime Kiara statement (the one about she willingly not ascending to a higher plane) means that the world caps at 4D, it says the oppose actually, that there are things beyond the 3D material plane of mortals (as in the human texture where normal people live) and that she is utter shit compared to those above so she prefers to stay among the 3D mortals to feel better with herself.

 

[Wankbreaker]

I may be wrong since this is advanced mathematics but I think the Klein cube principle can actually be used for any R^X beyond R^4, similar to the Klein bottle that Felix Klein also invented, so that doesn't really seem to limit it to only 4D, feel free to ask someone more knowledgeable in dimensional math like Ultima or DT though.

Every source I see says they can only exist in the fourth. It’s also commonly known to be a fourth dimensional object.

And again, the moon cell core exists in 4D INS

Will say at least that something that probably supports it not being limited only to 4D is the fact that Kiara is described as more complex than a 4D cube, which along with the 8D statement should indicate that the Moon Cell isn't really limited to only 4D.

It’s describing her mental structure,which is basically a big nothing burger. It could definitely just be similar to Tsukihime Kiara in which she can perceive a dimension above the 4th.

"There are many who have reached the status of a god as a human... but to think there could be one who surpasses a god while still human. No, seriously... what is that?! Her mental structure can't even be represented by a hyperdimensional cube!! It's like she’s got a universe inside her belly!"

「人の身で神に至ったものは数あれど……人の身のまま神を凌駕するものがいようとは。いや、そもそも……何ですかアレ！ 精神構造が超次元立方体でも表せねー！！ 腹ん中に宇宙作ってんじゃねーですよ！

Scaling-wise, it would also make sense if the Moon Cell wasn't limited to 4D only since it could apparently replicate Avalon (the sheath is in Artoria room) and recently demonstrated the ability to just straight-up pierce through the anti-purge defense granted of Avalon.

Avalon is never noted to be anti-purge defense, or shows up in OC3. In fact, it’s noted to be of a level beyond defense.

Also, the sheath itself isn’t 6D, just the protection it grants, it’s pretty much just a regular object without the TNR.

Ignoring the fact that it weaponizes the time-lock, which is

1. A 4th dimensional phenomena that works by manipulating the Timelock system, something Avalon is seperate from
and
2. Pretty sure this is part of the things it’s explicitly said to block.

In regards to the Arcueid statement, I don't think it really contradicts stuff since we know that nothing from Earth can destroy Earth due to the defensive systems in place that prevent even things with the necessary strength from being able to do it, this is the entire reason of why Earth goes out of its way to fight aliens, as these defensive systems don't apply to them, hence why Excalibur had to be created in the Inner Sea (Avalon) and universe's furnace to make it the strongest possible weapon, and from Lostbelt 7 we know that even a full power Excalibur used against an alien threat can't kill or significantly hurt ORT (and as result Earth was destroyed because of its strongest weapon being useless).

Arcueid says nothing in general,not just earth.

“defensive systems in place that prevent even things with the necessary strength from being able to do it,”

Which defensive systems? If you’re talking about the counter force, it explicitly does not act as a shield, it just summons guardians to get rid of threats, or influences human activity so that they get rid of the threats instead.

Even stuff like ORT is affected by the Earth’s texture, as it is affected by parallel world differences.

It’s also explained in the OP why destroying the “earth” in a singular timeline being equal to destroying Avalon is illogical.

And maybe it's just me but I don't see how the Tsukihime Kiara statement (the one about she willingly not ascending to a higher plane) means that the world caps at 4D, it says the oppose actually, that there are things beyond the 3D material plane of mortals (as in the human texture where normal people live) and that she is utter shit compared to those above so she prefers to stay among the 3D mortals to feel better with herself.

Except Kiara and Roa note that these higher dimensions are “another world”, and is the “outside”, and that she willingly returned to “this one”

 

[Wankbreaker]

わたしたちの宇宙は『時間』という概念によって成り立っています。本来、『時間』には過去も未来もありません。その軸を頼りにしているのは我々であって、


Our universe is constructed by the concept of "time."

In essence, within "time," there is no past or future. It is us who rely on that point of view.



The 4th dimension is what the entire universe in nasu is built upon.. which is consistent with literally everything above that being outside of the universe.

 

[ShiftCtrlAltDeleteTabFn]

Would the mooncell being called a Klein Cube be decent evidence for it being 4D?A Klein bottle is a 4D object, and im assuming nasu uses “Klein Cube” to essentially say it’s that in cube form.

there’s also this whole thing.

I don't think you can since I haven't found anything about a Klein Cube. I've only found Klein Cubics, which are different since they're equations that model higher dimensional surfaces, not the actual objects, from what I could find. Also, as @Expectro2000xxx said, they can go up to n-dimensions.

Klein Bottles are also different since they're a kind of manifold, which can also be projected up to n-dimensions.

Or something like that. I'm not an expert in this stuff.

Plus, the 8-D statement would override this anyway since it's an actual statement about the structure of the Moon Cell instead of equating it with something that doesn't actually exist and/or go up to n-dimensions. Actually, High 1-B Moon Cell sounds kind of fun...

 

[ShiftCtrlAltDeleteTabFn]

わたしたちの宇宙は『時間』という概念によって成り立っています。本来、『時間』には過去も未来もありません。その軸を頼りにしているのは我々であって、


Our universe is constructed by the concept of "time."

In essence, within "time," there is no past or future. It is us who rely on that point of view.



The 4th dimension is what the entire universe in nasu is built upon.. which is consistent with literally everything above that being outside of the universe.

Again, time being above everything else is not something that prevents there being more than 3 spatial dimensions.

 

[Wankbreaker]

Again, time being above everything else is not something that prevents there being more than 3 spatial dimensions.

Time constructs everything else.

Time is stated to be 4th dimensional.

Everything above the fourth dimension in the nasuverse is noted to be cut off from the universe, and the parallel world system, in which the Moon Cell is not.

There has not yet been a counter to this.

 

[Wankbreaker]

I don't think you can since I haven't found anything about a Klein Cube. I've only found Klein Cubics, which are different since they're equations that model higher dimensional surfaces, not the actual objects, from what I could find. Also, as @Expectro2000xxx said, they can go up to n-dimensions.

A Klein bottle does not have a inside or outside, the whole thing is a giant surface.

Cubic threefold - Wikipedia

en.m.wikipedia.org

A Klein cubic threefold is explicitly 4th dimensional.

Klein Bottles are also different since they're a kind of manifold, which can also be projected up to n-dimensions.

Or something like that. I'm not an expert in this stuff.

Plus, the 8-D statement would override this anyway since it's an actual statement about the structure of the Moon Cell instead of equating it with something that doesn't actually exist and/or go up to n-dimensions. Actually, High 1-B Moon Cell sounds kind of fun...

The 8D statement is kinda overrided by the fact that:

1. The Moon Cell core is a Klein cubic threefold,which is 4th dimensional

2. The core is located in INS, a 4th dimensional plane, and both BB and Hakuno manipulate INS to access the core in CCC and OC3 respectively.

3. The kanji used has the alternative definition of “level” or “layer”. It actually does not have a singular definition. Very few Japanese kanji do. So it could easily mean “eight-leveled barrier” or “eight layered barrier”. So there is an alternative explanation that honestly makes sense in the context of a protective wall.

 

[Vietthai96]

わたしたちの宇宙は『時間』という概念によって成り立っています。本来、『時間』には過去も未来もありません。その軸を頼りにしているのは我々であって、


Our universe is constructed by the concept of "time."

In essence, within "time," there is no past or future. It is us who rely on that point of view.



The 4th dimension is what the entire universe in nasu is built upon.. which is consistent with literally everything above that being outside of the universe.

Sound like abstract concept & perception of time than anything related to time as physical dimension, but again, as i have said, time being > almost everything is irrelevant

 

[Wankbreaker]

Sound like abstract concept & perception of time than anything related to time as physical dimension,

Time follows a “vector”, as noted by the scans in the OP. It is a dimension that exists.

INS (which is explicitly 4th dimensional) is noted to be a sea of time, and movement through the time axis is possible there.

but again, as i have said, time being > almost everything is irrelevant

It is when everything above the 4th dimension is explicitly noted to be outside or isolated from its effects.
Just saying “it is irrelevant” does nothing to further the discussion when there is a big fat contradiction.

 

[ShiftCtrlAltDeleteTabFn]

A Klein bottle does not have a inside or outside, the whole thing is a giant surface.

Yes, as far as I can tell, that's what a manifold is. The thing is, you can construct n-dimensional Klein Bottles, and to properly exist, they need to be embedded in (n+1)-dimensional space.

Cubic threefold - Wikipedia

en.m.wikipedia.org

A Klein cubic threefold is explicitly 4th dimensional.

Yes, but that's not a Klein Cube, like your scan states.

Also, as I have learned, it works in 4D Projective Space which is based on 5D Vector Space, so uh, that's something, I think?

Someone versed in this stuff, please help, my brain hurts...

 

[Vietthai96]

Time follows a “vector”, as noted by the scans in the OP. It is a dimension that exists.

What i mean is the texts you posted only, i know there is physical time dimension, well, probably i worded it badly, should be more specific, i just want to say that the specific texts you posted, which i replied to, is mostly irrelevant...........

It is when everything above the 4th dimension is explicitly noted to be outside or isolated from its effects.

I mean, it is true, for.....almost any verse (could be some obscure verses that idk is different but it isn't universal rule, just exception), but it mean as, you are outside time, so you not get influenced by it, but again you still can be within spatial dimensions, time is just dimension where events flow to form causality, outside time half of the time do not also mean you are also outside all possible spatial dimensions

 

[Vietthai96]

Someone versed in this stuff, please help, my brain hurts...

The moment walk into this verse, is the moment you accepted going to Hell

 

[Wankbreaker]

I mean, it is true, for.....almost any verse (could be some obscure verses that idk is different but it isn't universal rule, just exception), but it mean as, you are outside time, so you not get influenced by it, but again you still can be within spatial dimensions, time is just dimension where events flow to form causality, outside time half of the time do not also mean you are also outside all possible spatial dimensions

These higher spatial dimensions are noted to be separated from the universe, that is the thing. The Mooncell is not.

 

[Vietthai96]

These higher spatial dimensions are noted to be separated from the universe, that is the thing. The Mooncell is not.

Well, i just talked from technical standpoint, honest i did not play fate extra aside from watching some lore video like grand order so i do not know much, but isn't the the core is contained within the moon cell and the 8 dimensional statement referring to the entire moon cell not the core?

 

[ShiftCtrlAltDeleteTabFn]

Time follows a “vector”, as noted by the scans in the OP. It is a dimension that exists.

INS (which is explicitly 4th dimensional) is noted to be a sea of time, and movement through the time axis is possible there.

Tiamat

Tiamat is the antagonist of Babylonia. She, like all but one of the existing Beast-class servants, is currently unobtainable.

fategrandorder.fandom.com

The Sea of Life is states to be "essentially" a 4D pocket dimension, which is slightly different.

It is when everything above the 4th dimension is explicitly noted to be outside or isolated from its effects.
Just saying “it is irrelevant” does nothing to further the discussion when there is a big fat contradiction.

I want to point out that time explicitly doesn't work in Void/Imaginary Number Space.

 

[ShiftCtrlAltDeleteTabFn]

It is when everything above the 4th dimension is explicitly noted to be outside or isolated from its effects.
Just saying “it is irrelevant” does nothing to further the discussion when there is a big fat contradiction.

Also, BB (after absorbing the Moon Cell Core) and the Moon Cell see time as "flat" due to their higher dimensional perspectives.

And Divine Spirits with high enough Divinity are also explicitly unbound by the time axis.

How does that work with your ideas?

 

[Wankbreaker]

Yes, as far as I can tell, that's what a manifold is. The thing is, you can construct n-dimensional Klein Bottles, and to properly exist, they need to be embedded in (n+1)-dimensional space.

Yes, but that's not a Klein Cube, like your scan states.

Also, as I have learned, it works in 4D Projective Space which is based on 5D Vector Space, so uh, that's something, I think?

It’s a 3 dimensional object embedded in the 4th dimension (so INS, for this case).

Projective space has 1 more dimension than the objects they contain, and a “threefold”, is three dimensional

3-fold - Wikipedia

en.m.wikipedia.org

Could you also provide the source for the last sentence?

Someone versed in this stuff, please help, my brain hurts...

 

[Wankbreaker]

Also, BB (after absorbing the Moon Cell Core) and the Moon Cell see time as "flat" due to their higher dimensional perspectives.

As mash notes, past, future etc. are explicitly ideas created by lower dimensional lifeforms. BB and co are just viewing time in its original form. No contradiction here.

In essence, within "time," there is no past or future. It is us who rely on that point of view.

And Divine Spirits with high enough Divinity are also explicitly unbound by the time axis.

“時間軸” also means timeline,which fits more in what happens during the game. Amaterasu notices Hakuno in the future, and brings them to her time.

Considering even beings like ORT are affected by time based attacks like Tachyon Jail, the idea that time itself has no bearing can be considered out.

How does that work with your ideas?

 

[Expectro2000xxx]

Every source I see says they can only exist in the fourth. It’s also commonly known to be a fourth dimensional object.

Which sources? The super barebones wikipedia page you posted? Because based on the other Klein form that Felix Klein created (the Klein bottle) it seems that he was thinking beyond just a hypothetical 4th spatial dimension. I would prefer the confirmation of some knowledgeable member of this type of mathematics.

It’s describing her mental structure,which is basically a big nothing burger. It could definitely just be similar to Tsukihime Kiara in which she can perceive a dimension above the 4th.

"There are many who have reached the status of a god as a human... but to think there could be one who surpasses a god while still human. No, seriously... what is that?! Her mental structure can't even be represented by a hyperdimensional cube!! It's like she’s got a universe inside her belly!"

「人の身で神に至ったものは数あれど……人の身のまま神を凌駕するものがいようとは。いや、そもそも……何ですかアレ！ 精神構造が超次元立方体でも表せねー！！ 腹ん中に宇宙作ってんじゃねーですよ！

How is it a nothing burger to say that 4D can't represent her? When your entire point is that everything Moon Cell related caps at 4D? This directly disproves your point.

Avalon is never noted to be anti-purge defense, or shows up in OC3. In fact, it’s noted to be of a level beyond defense.

Also, the sheath itself isn’t 6D, just the protection it grants, it’s pretty much just a regular object without the TNR.

Artoria Avalon NP, Around Caliburn, grant anti-purge invincibility by projecting the paradise (Avalon) in the surroundings while also ringing the bells from paradise.

•Avalon: The Everdistant Utopia
The matching “scabbard” of the holy sword Excalibur. The wielder does not age, and injuries will also quickly heal.
After invoking its true name, Avalon dissipates as tiny particles into the air, and shields the wielder from all interference. No damage can be done to the wielder when a state of absolute defence is initiated. Even interference from the parallel world based on the Second Magic will be blocked. An “absolute defence” that can even repel the assault of True Magic, it is a True Magic in itself. No one can harm the tranquil King that stands in the land of Avalon.
When Avalon was unleashed, not even the King of Heroes could harm Sabwe.

Nasu also considers anti-purge the ultimate defense in the verse, hence why the EA was unable to hurt Artoria (as the NP specifies that anti-purge can block it).

Q: The terms "Tradition Protection" and "Anti-Purge Defense" come up all the time, what are these! <TG09>

Nasu: For tradition protection, if an attack does not follow specific rules it will not connect. This is possessed by Alice Kuonji's Ploy Kickshaw, for example. Basically, it's not an actual defense, per se, but something with restrictive conditions. Anti-purge defense is something we'll be talking about in more detail soon, so please wait just a bit longer on that one. For now, I can simply say that it is an ultimate defense against a level of attack that could even end the world.
Takeuchi: That term came about around the same time as the Panzer World Galient OVA ...did you really like the term that much?
Nasu: Enough to make it the most ultimate defense ever.

It would be completely pointless for the Moon Cell to recreate the sheath if it didn't have its special ability, similarly Artoria wouldn't have the need or compulsion of having the sheath with her if it was useless.

Which defensive systems? If you’re talking about the counter force, it explicitly does not act as a shield, it just summons guardians to get rid of threats, or influences human activity so that they get rid of the threats instead.

Da Vinci says that even an Anti-Planet NP would be unable to destroy the world, and then later Da Vinci and Holmes clarify that the reason is because of the existence of numerous defensive mechanism put in place so those from Eath can't truly destroy it, noting that aliens can do it because they aren't affected by them, hence why Earth had to create things capable of those alien threats that can destroy it.

Even stuff like ORT is affected by the Earth’s texture, as it is affected by parallel world differences.

It’s also explained in the OP why destroying the “earth” in a singular timeline being equal to destroying Avalon is illogical.

Same way as how Merlin is affected by parallel worlds despite being eternally inside Avalon, as there exists Lady Avalon/Proto Merlin, a parallel universe female version of Merlin. The Avalon of the Lostbelt 6 is also noted to be different from the one in Chaldea world, and the entire premise of that Lostbelt is that the timeline diverged and was doomed when the faeries inside Avalon were too lazy and didn't create Excalibur in that timeline.

Except Kiara and Roa note that these higher dimensions are “another world”, and is the “outside”, and that she willingly returned to “this one”

The planet is made up of more than just the human texture though, so the mortal/human world being 3D in nature doesn't then mean that the planet/world caps at 4D like you are claiming.

Holmes:
A satisfactory example, Miss Kyrielight.
The Tower stands at the end of the world, and its administrator wields the lance.
The question is, why does the Tower pierce the planet?
There is a theory that our world — the human world — is nothing more than one of the textured layers that wrap the surface of the planet, like a carpet.
To the planet, this is the consciousness of the intelligent lifeforms that reign supreme. In other words, our physical laws.
The “carpet” that maintains the laws of physics is our world. It is stitched to the planet so that it does not peel away.
This seems to be the phenomenon called the Tower of the End. It is also not limited to Britain.
There are multiple such pillars located throughout the world. One is the holy lance in the hands of the Lion King.

Reverse Side of the World [Others]
The place where the evil dragon Fafnir finally arrived at the very end of the novels. The Phantasmal Races, having understood that the Age of the Gods was over, ceded the Earth’s surface to humans and moved to this place. The world where humans currently live (including the laws of physics) is like a fabric that thinly extends across the surface of the planet. Beneath that fabric exist the planet known as “Earth”. On the other hand, the Reverse Side of the World is the world as it was before humans lived there… that is, the fabric of the era where Phantasmal Races strode the land. In other words, the Earth is the bottommost layer of the planet, and it is covered by the “Reverse Side of the World”—the place where the laws of the “world” as it once was reigns, and covering that is the “Present World”.
In the Reverse Side of the World, the Holy Grail cannot activate its function of “using the Third Sorcery”. In the first place, that function was for the sake of granting Shirou Kotomine’s wish. In other words, it is programmed to target humans, and doesn’t count Phantasmal Races as valid targets.
Jeanne d’Arc is a Heroic Spirit who, from the start, lost her human body long ago. Because of that, the chances of her reaching the Reverse Side weren’t completely zero… However, that is merely the kind of “not zero” like, as a comparison, somehow managing to pass through a wall with the tunnel effect, but the Throne where Heroic Spirits Exist is cut off from the time axis, so she effectively had an infinite number of attempts to try.

3. The kanji used has the alternative definition of “level” or “layer”. It actually does not have a singular definition. Very few Japanese kanji do. So it could easily mean “eight-leveled barrier” or “eight layered barrier”. So there is an alternative explanation that honestly makes sense in the context of a protective wall.

Wonderful how you are trying to use the exact same logic from one of the past failed Moon Cell downgrades, trying to break once again the rule against downgrading the tier 1 rating, even after just recently already having another attempt of breaking that rule rejected. You should honestly be reported.

 

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Kiara also created the Cage of the Fallen, where time simultaneously flows in multiple directions and it and space are measured from a one -dimensional perspective, somehow.

 

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It’s a 3 dimensional object embedded in the 4th dimension (so INS, for this case).

Projective space has 1 more dimension than the objects they contain, and a “threefold”, is three dimensional

3-fold - Wikipedia

en.m.wikipedia.org

Again, a Klein Cube doesn't seem to exist.

Klein cubic threefold - Wikipedia

en.m.wikipedia.org

Cubic threefold - Wikipedia

en.m.wikipedia.org

Also, it's a cubic threefold, which seems to be a little different.

Projective space - Wikipedia

en.m.wikipedia.org

Projective Space also does not seem to have anything to do with the objects it contains since it's defined by some vector space. For four dimensional Projective Space (P(4)), it's vector space is one dimension higher. (At least, from what I read, that's how it works).

Could you also provide the source for the last sentence?

Golden White Face | TMdict

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

www.tmdict.com

 

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The planet is made up of more than just the human texture though, so the mortal/human world being 3D in nature doesn't then mean that the planet/world caps at 4D like you are claiming.

We also have this statement about Divine Spirits existing in a higher dimension.

 

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Which sources? The super barebones wikipedia page you posted? Because based on the other Klein form that Felix Klein created (the Klein bottle) it seems that he was thinking beyond just a hypothetical 4th spatial dimension. I would prefer the confirmation of some knowledgeable member of this type of mathematics.

All the Klein forms have 4-th dimensionality related to it.

A Klein cubic threefold is also explicitly of the 4th dimension.

How is it a nothing burger to say that 4D can't represent her? When your entire point is that everything Moon Cell related caps at 4D? This directly disproves your point.

Her “mental structure” is not her “existence”, so yes, it is a nothing burger.

Artoria Avalon NP, Around Caliburn, grant anti-purge invincibility by projecting the paradise (Avalon) in the surroundings while also ringing the bells from paradise.

Nasu also considers anti-purge the ultimate defense in the verse, hence why the EA was unable to hurt Artoria (as the NP specifies that anti-purge can block it).

如何なる神秘で編まれたものか、鞘はエアの光を恐く弾き返す。防、御などというレベルではない




"What kind of mystery has woven this? The sheath fearlessly rebounds Ea. It is not at a level of defense or anything of that kind."



It is explicitly not at the level of “defense”.

It would be completely pointless for the Moon Cell to recreate the sheath if it didn't have its special ability, similarly Artoria wouldn't have the need or compulsion of having the sheath with her if it was useless.

It’s special ability is unrelated to the level of existence the sheath itself is at. The sheath is doing none of the heavy lifting here, it is the inner sea of the planet.

Da Vinci says that even an Anti-Planet NP would be unable to destroy the world, and then later Da Vinci and Holmes clarify that the reason is because of the existence of numerous defensive mechanism put in place so those from Eath can't truly destroy it, noting that aliens can do it because they aren't affected by them, hence why Earth had to create things capable of those alien threats that can destroy it.

The defensive mechanism is the Counter Force, which purely summons or influences human activity to get rid of the issue.

The world of Shinjuku is purely able to be destroyed because it is removed from PHH, meaning the CF has no care for it, as it won’t affect humanity.


I mean that world is already cut off from history!

No matter what happens there in Shinjuku, it won't have any effect on humanity whatsoever!

But uhh….. this does not affect Avalon, as Avalon is seperate from all parallel worlds, and time, and is also superior.

The whole entire point of the OP is to explain why this isn’t the case. You haven’t really provided a counter argument to that in particular.

Same way as how Merlin is affected by parallel worlds despite being eternally inside Avalon, as there exists Lady Avalon/Proto Merlin, a parallel universe female version of Merlin.

Merlin was not born in Avalon. No contradiction really arises here.

The Avalon of the Lostbelt 6 is also noted to be different from the one in Chaldea world, and the entire premise of that Lostbelt is that the timeline diverged and was doomed when the faeries inside Avalon were too lazy and didn't create Excalibur in that timeline.

Merlin clearly says it's a shadow projected from the real one.

とはいえ、ここはあくまでアヴァロンの跡。ブリテン異聞帯に映り込んでいる影にすぎない。


"That said, this is merely the traces of Avalon. It is nothing more than a shadow projected into the British Lostbelt."

It doesn't make sense for there to be more than one also, because it's also the source of all parallel worlds that exist upon the Earth.

(The scan for this is in the OP, so I won’t be providing it here.)

The planet is made up of more than just the human texture though, so the mortal/human world being 3D in nature doesn't then mean that the planet/world caps at 4D like you are claiming.

Sure. The argument is these cannot be reached from the multiverse, and that their level of existence is not above that of the multiverse.

Wonderful how you are trying to use the exact same logic from one of the past failed Moon Cell downgrades, trying to break once again the rule against downgrading the tier 1 rating, even after just recently already having another attempt of breaking that rule rejected. You should honestly be reported.

Entirely different evidence was provided here,which has no relation to this case. Provide counterpoints instead of hiding behind something that has no relevance here.