recursal/Fanatic-Fandom huggingface dataset:
Imperium Unitum

Vivat Imperium!

## Description

Imperium is a nation located in Europe and the South American coast. It is currently led and governed by Augustus Specyus and his cabinet.

## History

**Founding**

On April 19, 2022, Imperium was founded by Specyus, AlabamaSnail, and Germanicus. Its initial claim was that of the Roman Empire at its greatest extent, but it slowly expanded to encompass new users. These new lands were separated into multiple provinces that individual governors had autonomy over.

**Icelandic Raids**

On April 26, 2022, Imperium experienced its first barbarian raid, consisting of two Iceland members (88Nick880 and oDababu). They were quickly dealt with and sent back to Iceland. The next day on the 27th, after forming 7th Column, the entirety of Iceland participated in a more organized raid of Imperium. Yet again, they were defeated, with Imperium occupying their territory and sending them to northern Canada. On April 30, 2022, one final raid was planned and executed by the Icelanders while in Canada, but was countered and destroyed with the help of an Imperium loyalist within their ranks (Deka).

**The Gaulic Conspiracy**

On May 16, 2022, the province of Gaul, unhappy with Imperium’s refusal to expand their province into Germania and Spain, had the nations of CES, TBC, and The Federation help them overthrow the empire. Imperium was forced to relocate to South America.

**The Foretold Reconquest**

On July 7, 2022, Imperium reentered Europe due to the inactivity of the French and retook the majority of it's former territories. There was no resistance and Imperium was congratulated by its previous enemies.
Republic of Greenlandia

## Origins

The official claims of Greenlandia are only made of Greenland. The flag used at this time was the regular Greenland flag.

Greenlandia was originally founded by Trystan, who was banned from Earthcraft due to harrassment. The original Greenland was not very popular, and had a negative reputation to many nations. Not long after Trystan's ban, Cheeseeater took over Greenland. Then Cheeseater was forced out of Greenland by TF and Greenland was given to Crack. Then there was an election for president of Greenlandia, but it was eventually decided that ownership of Greenlandia would be divided between Cheese and Crack. Then after threats by Ethan it was split 3 ways between Cheese (33%), Crack (34%), and Ethan (33%) (Ethan is/was a friend and much-needed bodyguard of Cheese). Ethan only joined because of Cheese, with no intentions of actually doing anything for Greenlandia. Likewise, Cheese and Ethan quickly neglected Greelandia and the duties of being a leader. Crack supposedly did his best, but there is only so much one can do after being robbed of all his resources. Cheese supposedly left to be a nommad and a citizen of the new USSR (formerly The Federation). It is unclear what Crack did after being left to lead what was left of Greenlandia by himself. Due to Cheese's horrible reputation, actions, and diplomacy, (as well as Crack's poor reputation) Greenlandia became victim to widespread griefing and destruction. Not much is left of the buildings. The place is in ruins (at least they still are on June 24th 2022). The few citizens still there are mostly not active on the server anymore, or forgot they technically still have citizenship. Crack, for example, has many different citizenships around the world. It is clear that due to Cheese's inability to be a leader (and even just a decent person), as well as Crack's lack of precense in Greenlandia, there is nothing left but ruins and desolate snowy mountains.
The Holy Kingdom

The flag of the Holy Kingdom

The Holy Kingdom is a nation located in central Asia, which was formed after the French annexation of the Papal states following the Roman-Potago War. Its government is a Christian Theocracy led by awp4444, a self proclaimed schizophrenic. The country is a defensive pact with Fanrong and Atheau to which it neighbors.
Infernum

Infernum is a colony/nation located in the Nether. It is currently led and governed by loteman. Infernum is filled with greenery, foliage, and water!

## History

###### **Imperium Portal**

Before The Gaulic Conspiracy, Imperium had a working nether portal located on Crete (Which was lotemans base at the time), When loteman heard that Gaul is going to declare independence, He preferred to run to the nether and break the portal then to stay with either of them, so he set up a nether colony and called it "Infernum" (The rest of Imperium escaped to South America)

###### **Peoples Backlash**

Soon after loteman had set up chests and was ready to start terraforming, he had gotten all of his items stolen/burned by Joey585 and Fredboys, There was a huge argument on why loteman would run to the nether, loteman said that he preferred to live in the Nether than to stay with traitors or go to brazil. He was later forgiven by both RDS and Imperium.

###### **The Incident**

After the EarthCraft server updated to 1.19, the proxy attempted to generate the nether again from 0,0 out, luckily admins stopped it but it had engulfed half of Infernum, Admins promised to compensate, And they did! they had terraformed a large area where the base had been lost and added water, The admins had also built a large nether dome with grass and trees.
Omnicollapse

Omnicollapse is a hypothetical number, meaning that it is undefined, and is an idea of a number rather than an actual number. For Omnicollapse to be defined we would have to have omnipotent power. Its collapsed, defined counterpart is Weak Omnicollapse

## Cognitive-Theoretic Function

Suppose that a function Շ(n) exists that creates a computer theoretically able to compute absolutely anything, within an equivalent **Level of Thought**. For example, a Շ(0) computer would be able to compute everything up to **The Box**, and a Շ(1) computer would then be able to compute everything up to ∀+.

Շ(n)'s proper output would be the absolute highest number computable within it's equivalent Level of Thought. Anything beyond Շ(2), however, would only be considered a **Level 2** collapse of such due to the nature of levels beyond such; however their full uncollapsed forms still fully exist; and in fact their uncollapsed forms exist within this reality having bypassed the **Level 2** restriction of being bound by fictionalized layers of such.

We can then define a number henceforth known as the **Cognitive Fixed Point** (shortened as CFP, symbol is ♝) which is simply defined as the fixed point of Շ(n).

## Uncollapsable Numbers

So far, all of the numbers we have made were able to be collapsed into a **Level 2** form, one way or another. However, this will change quickly, as we now define **Omnicollapse** itself as a number so vast, it cannot be collapsed into **Level 2** thought and would instead be forced to collapse through every single level and halt at **Level 3**. Of course this is not possible for us, but this is just the idea of a number that would have those properties, it is a hypothetical number.
The Federation

## Description

Throughout the ever-changing climate of EarthCraft, The Federation stands firm. With it's claims to Canada and the United States west of the Mississippi river in addition to Russia, The Federation's priorities lie in providing land to those who need it, especially new players who may notice the lack of land, and are forced to join us since we own all of it. They have a strong alliance with The Blue Federation who has helped them greatly in the past and The Federation aspires to follow in their footsteps towards providing freedom and assistance to those in need.

As of mid-June 2022, the nation is now known as The Union of Sovereign Socialist Republics (USSR).

## History

From humble beginnings as four separate groups, all with the supplies needed to supplement each others growth, The Federation flourished and saw it's great growth through partnership.

It's parent countries, Alaskan Republic of America and the Flat Earth Federation (residing in Alaska and central Canada respectively) decided to merge to form the Northern Federation on April 26, 2022. Though still a smaller nation at this point, The Federation was starting to take shape.

Under the new name and larger population, the Northern Federation turned to Russia for a fresh supply of land, quickly spreading to own the whole country.

On May 8th, 2022 the Mormons joined The Federation adding Hawaii to their growing land. The Union of Shaburburist Socialist Republics who heavily relied on the Mormons as their main military and resource supply followed in their footsteps just hours later. This cemented the majority of the land claims that The Federation has today, adding all United States land west of the Mississippi river besides the state of Washington in addition to claims in Africa, England, and South America which were later rescinded. They then took the name of The Federation.

Finally, on May 12th, 2022, The Federation announced it's annexation of the Republic of the Puget Sound, taking their claims to the state of Washington and British Columbia.

## Government & Territories

### **Pre-Democracy Government**

In the past The Federation used a minister system government. Each minister was responsible for some Federation land as well as taking on a more specific role in the government. The role of Prime Minister's role was mainly overseeing the business of the other ministers as well as being in charge of diplomacy and response to conflict.

### **Transformation to Democracy**

As of the end of May 2022 though The Federation would start to transform in to a representative democracy. Hosting their first election on the 31st of May.

#### **First The Federation Election Results**

Presidential Election Results:
 Prorickey

Vice Presidential Election Results:

Head of National Security Election Results:

 BrooklynLodger
 Rac
 TheRatMan
The Yuan Parlamentarium

The Flag of Yuan

## Description

The Yuan Parlamentarium (Yuan) is a mid sized nation located in western china, mountainous in terrain the harsh terrain has been a turn off of many players, but a strength to those who choose to stick with it. Most interestingly, Yuan is one of (if not the only) Parliamentary Monarchy on the server, with them currently having (but not publicly releasing the details of) their Emperor.

## History

The History of Yuan closely follows the history of its leader, TheNewCole. After a series of disputes within TBC leadership, most of them following The Gaulic Independence war Cole left to join Raven Republic, wherein once again more leadership disputes occurred, and after a partial departure/partial kick out, the Yuan Parlamentarium was founded. (Cole Insert more text here once you gather the relevant information - Past Cole)

## Government

The Yuan Parlamentarium, like its name suggests is primarily a parliamentary system under a symbolic Emperor, though governed by "The Parlamentarium Ministry of Yuan" (PMY) Its members are voted upon on the 15th of each month from all eligible candidates (citizens and invitees from certain nations. However the unique thing about the council is its direction, the Yuan Parliament practices "Equal Inequality" wherein members all hold the same amount of power within the council, however the type of power is not the same. Leadership of the council is divided up into 3 Ministries, Diplomacy, Defense, and Planning, with each ministry having its powers over the others.

## Trivia

* The Parliamentary Council of Yuan is not the first council designed by TheTrueCole, as he also formed the groundwork of the TBC council government as well
* As a direct result, the design PMY addresses many problems that Cole had with the TBC council and has been described as a "counter" to the equal council type of governance
* The Yuan Parlamentarium is one of the few nations whose borders cannot be accurately drawn using the Mapchart software, requiring outside tools for them to be drawn
Furui-Fanrong

Not to be confused with Fanrong.

## Description

Fanrong is the large nation centered in Eastern Asia. This nation is split up into multiple districts each being controlled by a specific leader. Each of these districts will eventually have a special exported material, one example of these would be Jin-de exporting gold to other nations and districts.

## History

The nation of fanrong started on April 25, 2022 at 22:22 (10:22 pm) with a donation of what is the two southern islands of real world Japan which is now named the Jin-de district from a player named Napalm\_Bomber.

Later, Aerbax, the founder, decided to take over two peninsulas nearby in china which is now called the Zuanshi and Tiě district.

Soon after that, production on the capitol city of all of fanrong, Wanmei, had begun, starting with the building of the easternmost international island.

Soon after, the USSR, gave up territory in real world china which was immediately taken over by Fanrong and converted into a wood farm meant for the continued production of the capitol. This section of territory is now called the Mucai district.

Much later, the Fedaration (at this point was still called the northern Federation) had decided to take over land farther west covering the eastern half of russia. In an attempt to give the Federation-Fanrong border more of a favorable buffer for Fanrong, Aerbax decided to buy coastal areas of new Federation for a stack of 64 diamonds. This created the Huanchong district, also known as the bufferpoint.

Durring the Huanchong transaction, Fanrong decided to take more land in an effort to connect all of fanrong, namely taking over what is now the Duo-shan district.

The Nongye district which is real world Taiwan was donated by the TBC as an act of goodwill after who owned it was called into question by Aerbax.

Much later around May 26, 2022, at 22:26 (10:26 pm), a player named Cyril\_046 decided to join the Nation of fanrong bringing what is now known as the Yáhgānmrè district with them.

The fall of Napalm\_Bomber marked a massive turning point for the people of fanrong. they had finally completed their "Manifest Destiny" without breaking their religions primary rule and had taken all of real world Japan.

After a cataclysmic disaster ending all life on earthcraft, the people of fanrong migrated through a rip in space time returning them to the dawn of this world. it was deemed VoidedSky by the false Gods of the south (western africa spawn region). Unable to return to their homeplace in this world, they settled for another island location. Great Britain.

## The Ming-Yun (Shu de Shinri) Religion

Ming-Yun was the primary religion of Old Fanrong. its primary values had prevented them from involving themselves in any external conflicts that didnt affect any of those native to the regions they controlled. This religion is of of tranquility and peace. while they did pray to a God, it wasnt one of tyranny, but one of complete indifference to those that either worshipped them or did not. this god reflected the only rule of its religion, it showed a want not to me shown blind faith but only requires respect. Shu de Shinri
7th Column

## Backstory

7th Column is a group of players, PenguinSAD, 88Nick880, oDababu, habbys, Evo1015, and 2 unknown members. 7th Column was created after 2 of the members, Nick and Dababu, were killed by Imperium Unitum. Before they died, they managed to kill over 6 Imperium members. The cause of this first event is disputed. Nick and Dababu went to Iceland, and quickly joined up with the other members of the 7th.

## First Invasion and Banishment

A couple days later, 7th column once again raided Imperium. Once again, they were defeated, but not before killing multiple Imperium members. After this event, Imperium invaded Iceland and forced 7th Column to flee. When 7th Column fled to Canadia, Nethermob(555), a friend, gave them safety by letting them stay in Hudson Bay under surveillence.

## Second Invasion

As 3 days went by, 7th Column slowly build up their resources, obtaining villagers and amassing diamonds. 2 days after the banishment, the plan was made. 7th Column would stage one final invasion, destroying Imperium once and for all. Knowing of MushiMango, they asked Nethermob to send him an invite. Mango agrees to join the invasion force, and the final plans are made. Unknown to 7th Column, however, Mushi reached out to Imperium, giving them details about the invasion and agrees to betray 7th Column for Imperium. On the day of the invasion, Nethermob decided to join, as a passive observer who would only attack if attacked first. When 7th Column met with Mushi, they all headed to Sardinia where the combat took place. As 7th Column began to attack, the betrayal took place. Now outnumbered and taken aback, the 7th Column was destroyed. After the battle, all members of the invasion left for unknown amounts of time.
Kieven Rus

About the nation:

* Is a Nation in Eastern Europe
* Is a Kingdom
	+ Capital is Kyiv

History

One day, Soripheal had a city, he moved, then got the money to make a nation, then the town of Kyiv was made, then, the resting beast, arose, people teased him, but he was fine.

Successor

Currently, we have no idea who will succeed Soripheal.

System

A Communistic Principality

Religion

Free religion
Fallen Empire of Great Doria

The Fallen Empire of Great Doria (FEGD) is a nation in the Middle East led by Ldogwaffle. This nation worships the One True Door and follows the religion of Dorianism.

*This nation is not to be confused for the Dorian Empire from EarthCraft Season One*

### History and Founding

The FEGD was founded on May 24, 2023 by members Ldogwaffle and BroaderShip6655. This nation is based off of the Dorian Empire from Season One, though it has many differences to that nation. Primarily, the rules of the Dorian Religion drastically changed.

### Location

The FEDD is located in the Middle East, more specifically the countries of Saudi Arabia, UAE, Oman, and Yemen. This location was chosen due to its flat land which is ideal for the building of the 128x128 pyramid known as the Dorian Complex.

### Members

As of June 13, 2023, there are 7 members of FEGD

### Ranks

The Messiah - Ldogwaffle

High Dorian Priest - BroaderShip6655

Dorians - C0sm1n, Boogor Man, Galt321, Starma, ThaKidKyle$
Sea of Nurnen

The **Sea of Nurnen**, formerly referred to as the **Caspian Sea**, is a significant body of water situated in the northern Middle East, specifically within the region of western Asia. In actuality, it is classified as a lake rather than a sea, boasting vast proportions. Notably, it stands as the largest river biome on the server.

Economically, the Sea of Nurnen serves as a thriving haven for several nations that border its shores. The First Empire of Atheau, Mordor, and The Holy Kingdom, in particular, benefit from the economic opportunities and resources offered by this expansive water body. These nations recognize the strategic importance of the Sea of Nurnen, utilizing its resources and proximity to foster economic growth and development within their respective territories.

## Name Change Reason

On June 13th, 2023, Mordor, a nation situated near the Caspian Sea, initiated discussions with neighboring nations regarding a proposed name change for the body of water. Mordor put forth the suggestion to rename it the Sea of Nurnen, derived from their own province known as Núrn. Following deliberations among the nations bordering the Caspian Sea, the proposed name change was accepted and officially implemented. Henceforth, the body of water is recognized as the Sea of Nurnen, paying homage to Mordor's province and reflecting the consensus among the neighboring nations.
Library of Constantinople

Frontal View of the Library of Constantinople

## The Library of Constantinople

The Library of Constantinople was the first public library built on the server, and was located in Constantinople. It is the best library in the world and has the most books as well. Containing classics in fiction like 1984 by George Orwell, and The Fembible and Non Fiction books such as the Travels series by Marpion Pomodoro and the best selling book of all time, The Holy Bible, it comprises of most of the servers intellectual knowledge. As the center of knowledge donations have been made for it to continue its operations. The highest of these donations was 14 diamond blocks by Neixy.
Pensacola

## Description

Pensacola is a large city located in the Commonwealth of Eastern States around the Florida Panhandle. The city is connected to the CES rail network and features a canal that goes to Detroit. It also features an underground subway that has an ice path to Detroit, and a railroad to Atlanta. Pensacola has a very small population of just 2 players, Sethf22 and Goofy\_43. While Pensacola never had any mayoral elections, Sethf22 was pretty much the mayor, due to literally no one else living there.

## History

Pensacola was founded the on day the server started, 4/22/22, by Sethf22. Pensacola steadily grew in size, until about mid January, when Sethf22 stopped expanding it. Pensacola was slightly griefed on April 23rd by 3 players, but thanks to Bearofbusines and Fankaz, there was very light damage. Another instance of griefing was when MooseManiaMan and Cheeseater stole Pensacola's 2 beacons and stripped some trees.
First Empire of Atheau

The Flag of The First Empire Of Atheau

The First Empire of Atheau, or commonly referred to as the FEA or simply just Atheau, is a large predominately Asian country that spans from eastern Europe, through all of northern Asia, to Alaska. It also holds territory in parts of Mexico.

It borders the First Republic of Poland to the east, and the Roman Empire, Mordor, The Holy Kingdom, and Fanrong south of it's Asian territory, and also borders Kingdom of Aylis and Deseret both border the Alyeska territory to the east and to the south of that territory is Sunset Dominion. Down in its Mexico territory has Sunset Dominion on its northeast and the Golden Circle of Aurelius to its northwest and south. This makes Atheau border the most countries in the world, bordering 9 different countries.

The country's current has a population of 15, with 11 towns (some of which hold players), the largest ones being the Ravnya, Rechnaya, and Ramil.

It is separted into 3 distinct regions, being the East, the West, and Alyeska. Mainland has 3 primary cities for each side. The aforementioned cities Ravnya, Rechnaya, and Ramil for the East, and Apochayva, ???, and ??? for the West.

## Leaders of the Empire of Atheau

 Cuvsly
 Cuvsly
 Perstob

## **Foundation | Senlin Gongheguo to Atheau**

The First Empire of Atheau, originally Senlin Gongheguo, started off as an anarchist territory located in the far eastern parts of Russia. Senlin Gongheguo started with 5 members who would build and rule over the 5 cities of Senlin Gongheguo; Impea, Areia, Voida, Atheau, and Udrea. Senlin Gongheguo's plans would shift upon a council vote to create a government that was once at the back of the mind of the Parliament of Novgorod. Wildersans122 and Cuvsly were the opposite of one of another; While Wildersans122 wanted to remain small and insignificant Cuvsly wanted to restore the Empire of Novgorod as part of the Final Stretch (otherwise known as the Restore the Empire Plan or the Final Empire Plan.) Wildersans122 would only rule for 3 days before the council voted to hold a vote for the Second President of the Socialist States of Atheau.

## **First Election**

The First Election of the Socialist States of Atheau was the most eventful election. The PDSP (People's Democratic-Socialist Party) and RSP (Revolutionary Socialist Party) would merge to form the UASP (United Authoritarian-Socialist Party) which believed that the Final Stretch could be accomplished. The UASP became the dominant party of the Socialist States of Atheau for the 2 weeks it was around for before being disbanded due to differences in ideas. 3 candidates would drop from the first round after all 4 candidates tied which led to a battle between the UDWP and UASP. Upon the UASP's victory, the Final Stretch would finally become a reality.
Nations of the World

EarthCraft has a lot of nations, many recognized and some not so much. This base is dedicated to a list of every country declared by a user.

**The Federation**

The Federation was founded in May 8th 2022 under the name Flat Earth Federation. Then the Flat Earth Federation merged with The Alaskan Republic of America to form The Norther Federation. Then after a few more merges with lesser-countries we have The Federation.

The Federation borders are expansive, spanning across North America, Africa and Eurasia.

The map listed is not completely accurate in the far asian countries as fanrong claims coastal land farther north into Russia

**Republic of Democratic States (RDS)**

RDS declared independence from **Imperium Unitum** May 16th 2022 under the name Junta de Gaul, then changed its name a few more times until we arrive at **Republic of Democratic States**.

RDS also has a claimed section in Africa called the RDS Reserves. They've claimed this land and have plans for it but have not moved into or developed

RDS spans over North and South America, Asia, Africa and Europe.

**Commonwealth of Easter States (CES)**

The CES was formed on April 19th 2022 under the name **Commonwealth of Eastern** **States**. They were a combination of 4 different people's claims to land. Some expansion later and we reach their current borders.

The CES spans over North America and Africa.

**Fanrong**

Fanrong was formed in April 25th 2022 with the name Fanrong where Japan donated 2 southern islands. Some expansionism later and we have Fanrong today.

Fanrong spans over only Asia, but quite a large chunk of it at that.

**Vassal of Monderninity (VoM)**

VoM was formed. That's all we know. They donated the 2 southern islands to Fanrong.

VoM spans over Japan.

**Aerial Kingdom of Asia (AKA)**

The AKA popped into existence. It has 2 pieces of China.

\*NOT DONE I NEED SLEEP\*
Multi-Conclusion Logic (True Logic)

this is probably as far as I'll go in formalizing HG lol

the page is pretty poorly made sorry abt that

also this isn't a lot of work, next pages gon be about HGAL submissions and spectrum theory, but this is also kinda important

If you have any problems with lmk

## Introduction

Multi-Conclusion Logic is the language HG (well, most of it) operates on, formalized to an extent of being on par with any other deductive system in terms of formality. It is an extension to first-order logic, similar to set theory, but the key differences are there, so imply first-order logic and language active in this as well.

### Language

>=>, <=> - referrents (x => y <-> x refers to y)

X1- The statement referred to in the statement itself (self-referential) (p: "p" <-> "p" = X1)

Xn+1- The conclusion of Xn (conclusion of P = "P= T/F" )

XI- The statement (XI <=< XU)

XU- The conclusion (XU <=< empty)

### Various Proof

Since there isn't a lot more to cover, let's just continue with the most important part.

Proof 1: Consistency

Let's take the statement "this sentence is false".

First, we reword it to X:"X=F"

Notice that "X" = X1

Considering X\_n, we see that X\_1 is not defined as being false, or true, therefore it contradicts the original statement X, and that means that X is false.

From this, we can derive that a self-referential statement X with a truth value arises iff:

1. X => []1 ( "[]" means any amount of statements referred to in X)
2. (if X is false) X =/= []1
3. (if X is true) X = []1

Which is the definition of any logical antimony, meaning that all self-referential statements are consistent.

Proof 2: Completeness

1. P: "P is unprovable"
2. P\_2: "P=T"
3. P\_n: "P\_(n-1)=T"
4. P\_1=T (proven) -> P\_1 is provable -> P=F

This is a similar case to the consistency proof, so don't mind it a lot.

This is pretty much all you need to know about it, by the way if you didn't get anything, ask me: Solarii [Писатель] # 3653 on discord
Limits Limit+ (Lᴸ+)

This definition uses the term "limit" as defined in LL.

## Unbounded CS

CS is a level 2 collapse of a level 3 concept (definition strength). But what if we took this further? What if we allowed this concept to affect thought levels?

I will define Unbounded CS (UCS) as a version of CS that can access any thought level, including concepts that surpass thought levels. We can then define AUCSL as ACSL as defined within LL, but where CS is replaced with UCS. UCS would also be able to enable paradoxes and ignore paradoxes.

## Definition

**LL+ is then defined as the limit of all limits (AUCSL)**. This would, for example, be larger than a level 5 version of LL (if collapsed to level 2), as the AUCSL means that it can surpass an level.

It should be noted that this is collapsed to level 2 by necessity.
Gl函数

## Gl函数的定义

1. Gl(n)指的是用n个符号、数字或字母等记号所表示的最大值。
2. Gl(n)的迭代次数不超过Rayo^n(10^100+n)+n^18.
3. Gl{0}(n)(m)=Gl(n).
4. Gl{a}(n)(m)=Gl{a-1}(n)(Gl{a-1}(n)(Gl(...)...)...).<m个Gl()>
5. Gl(n,m)=Gl{Gl(S(n,m))}(Gl(m))(m).
6. Gl(n,m,q)=Gl{Gl(S(n,m))}(Gl(n,m))(Gl(n,m)).
7. Gl(a[b]c)=Gl(a,a,a,a,...,a)<U^b(c)个a>.
8. Gl(a[b,c]d)=Gl(a[b]a,a[b]a,a[b]a,...,a[b]a)<U^b(U^c(d))个a>.
9. Gl(a,b[cKd]e)=Gl(a,b[c,d]b[c,d]b...b[c,d]e,c[b,d]c...[b,d]e)<Gl(c,d)个[c,d],Gl(b,d)个[b,d]>.
10. Gl(a,b[cKdKe]f)=Gl(a,b[cKd]f,b[cKe]f).
11. Gl(a,b[cKKd]e)=Gl(a,b[cKcKcKcK...Kc]e)<d个K>.
12. Gl(a[bMc]d)=Gl(a[bKKK..KKKc]d)<Gl(a[bKKK..KKKc]d)<Gl(a[bKKK..KKKc]d)个K>个K>...<Gl(a[bKKK..KKKc]d)个Gl(a[bKKK..KKKc]d)>.
13. Gl函数内部的[]里展开方式与鸟之记号相同。

* 例：
* Gl(2)=g(9)
* Gl(5)=Gl(9)=......=......=??
* 1次 2次 ...次 Rayo^5(10^100+5)+5^18次
拉差尼·西派万

**拉差尼·西派万**（泰语：รัชนี ศรีไพรวรรณ，1930年3月11日 - 2014年4月15日）是泰语学家，作家和学者。她是泰语教科书系列《玛尼和她的朋友们》的作者，从1978年至1994年在泰国1至6年级全部小学使用。她的书也被用来在澳大利亚制作泰语课程。她在2013年获得了Narathip奖。

西派万出生在泰国玛哈沙拉堪府的哥颂披柿县。她曾就读玛哈沙拉堪小学。然后她参加Wang Chankasem教师培训学校。她还在曼谷的教育学院学习，现在被称为诗纳卡宁威洛大学。

拉差尼·西派万于2014年4月15日在曼谷维柴尤特医院逝世，享年84岁。

参考
--

1. ↑ 1.0 1.1 1.2 1.3 1.4 1.5 Template:Cite news
Postfinity

**Postfinity** (∰) is defined as the limit of the []-mathematics system laid out by Outerconst.

## Notations

For the sake of simplicity, different forms of []-mathematics will be assigned a number. A-mathematics will be defined as M1, B-mathematics will be defined as M2, and so on.

## Definition

According to the aforementioned article for Outerconst, Outerconst itself is defined as B0. This already sets up obvious extensions, such as Bω and BΩ, however due to the nature of different types of transcendent mathematics, none of them will surpass M3(0). Once more, this sets up a transfinite meta-hierarchy of transcendent []-mathematics, with extensions such as MΩ, therefore **∰** is defined as the first number fully transcendent over all transfinite numbers using []-mathematical notation.

## Set-theoretic definition

Let it be that the set of all finite []-mathematical indices is denoted as **∀**. This set is defined as {M1, M2, M3...}, and so on and so forth with no arbitrary endpoint. **∀**, being the set of all finite mathematical indices, is of course contained by **∀ω**, the set of all []-mathematical indices defined as {**∀ω**, ∀ω+1, ∀ω+2...} and so on and so forth. This already sets up a transcendental hierarchy of ever-increasing transfinite ordinals denoting ever-larger and more infinite sets of []-mathematics.

Let it also be that the set of all transfinite, inaccessible, absolute, immaterial, non-existential, and total numbers is denoted as ௹.

Let it also be that the set of **all** transfinite, inaccessible, absolute, immaterial, non-existential, and total []-mathematical indices is denoted as ⇰⨷. As such, the logic statement follows that ∰ Ω> {௹ ∪ ⇰⨷} (∰ is absolutely infinitely above the union of ௹ and ⇰⨷).
Alliance of Small Nations

The Alliance of Small nations is a partially defunct and relatively inactive alliance group created by the Dorian Empire to further diplomatic relations.

## Alliance of Small Nations

### Members (Current and former)

Dorian Empire, Tequila Empire, Scott's Land, Aerial Asia, AUW Vassals, Puget Sound

The concept of AoSN may have been good, however, many nations had developed past a point where they could be considered members of the alliance, and with a general lack of new nations at the time of creation, the group fell into irrelevancy, and some of the member's groups ceasing existence. While the group does still exist, it is far from it's former glory and isn't formally recognized by most nations as of now, even the members who's nations still exist. The group was also used by AUW to acquire more vassals for their nation.
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泰语教学课本《玛尼和她的朋友们》（มานะ มานี ปิติ ชูใจ）非官方Wiki
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Manee icon.jpg玛尼Mana icon.jpg玛纳Piti icon.jpg比迪Chujai icon.jpg楚哉Weera icon.jpg威拉

* 书目：一年级第一册 • 一年级第二册 • 二年级第一册 • 二年级第二册 • 三年级第一册 • 三年级第二册 • 四年级第一册 • 四年级第二册 • 五年级第一册 • 五年级第二册 • 六年级第一册 • 六年级第二册
* 原作者：拉差尼·西派万
Surpition (s*)

Surpition (s\*) is a number defined by Goodels to beat EIG520's number Reduk. Its smaller counterpart is Subition (s-).

## Definition

* Nothing cannot be considered a "thing", regardless of anything in any definition that tries to counteract this.
* s\* is beyond all things that have some relation to some other thing, regardless of anything in its definition to counteract this.
* s\* ignores anything that hinders its size or definition with maximum strength.
Conkept Surpassion Proof

Conkept Surpassion Proof is a proof by Goodels that shows that we can go beyond Conkept using Serge's 'thought levels' . 'Object' and 'property' here are both defined in the Conkept definition.

## Proof

**Argument:**

* For all properties, there is a object possessing it that is lesser than Conkept.
* An object existing on a certain thought level is itself a property.
* Therefore, Conkept surpasses all other objects regardless of thought level.

**Response**:

* Conkept must be an object.
* Conkept has a definition .
* A definition must exist in real life (eg. written down or thought of by someone), or a definition could   be defined by another definition (eg. a rayo's number type situation).
* Therefore, Conkept must exist on a thought level.
* The n+1th thought level can be used to define the nth thought level with absolute power.
* Therefore the n+1th thought level can define a number bigger than any number you chose from the nth thought level.
* **Therefore, Conkept can be surpassed by using the above thought level, or a collapse of the above thought level.**
Limits Limit (Lᴸ)

Limits Limit (Lᴸ), is a tier IV number, made by Goodels. It uses Counter-Strength to surpass previous numbers.

## Max Counter-Strength?

When we try to have a limit of CS (counter-strength), we run into a problem. When we define "Max CS", it is automatically going to be smaller than 'Max CS (CS 1)'. We can continue, creating recursions like 'Max CS (Max CS (Max CS (....)))', or even more crazy recursions like, 'beyond the limit of 'Max CS (Max CS (Max CS (....)))' (Max CS)'. I will now define anadromic CS limit (ACSL) as the level of CS, where no 'recursions' of Max CS can describe it, which would make it equal to things like (ACSL (Max CS)).

## Limits

A limit here is defined as the end of something, where something could be literally anything. for example, there is a limit of the finite numbers, a limit to the amount of 2cm3 balls that could fit into a 10cm2 cube, a limit to countable sets, and so on.

## Definition

**We can now define LL as the limit all other limits (ACSL)**. This would include things like the limit of thought levels, the limit of hypersystems and even hypergoogology itself. It should be stated that this is collapsed to level 2 by necessity.
Pseudo Finality (p.F)

Pseudo Finality (p.F) is a tier VI number, it is extremely meta and uses some very powerful concepts.

## Hardware and Software

If we look at Hypergoogology, it is seemingly made of 2 main parts. These parts are the "software" and the "harware". I will denote what I call the "software" as HG:s and I will denote what i call the "hardware" as HG:h. HG will denote Hypergoogology itself.

So first I will start with HG:h. HG:h is the external abstract factors within our reality that contribute to HG. The main (but not only) factors to HG:h would probably be the logic that governs HG, our ideas of "size" and "number" ect... I call HG:h the "hardware" because that's exactly what it is. HG:h is the circuit boards, whereas HG:s is the programs within the computer.

So, what is HG:s? Well, HG:s is all things that take place under HG:h, things like definitions within HG are HG:s

## Bribery

"Bribery" is when some definition in HG:s uses a "bribe" to make its definition more true within HG:h. A bribe in this case could be literally anything in a definition within HG:s that tries to brute force affect HG:h. An example of bribery would be if a definition said "this definition ignores all other definitions" or if a definition says "this definition will be prioritised above all other definitions".

## Definition

* p.F has the strongest possible form of bribery, which affects all of this definition including this.
* p.F has a bribery so strong such that it affects HG:h to make it the largest number.

## Note

If you look closely, this definition backs itself up. By claiming it has a strong bribery, it gives itself a strong bribery within HG:h, which then gives itself an even stronger bribery and so on. Of course this number does not actually affect HG:h, but it makes a strong enough attempt to where it's very strong.
Full Opux (!!!)

Full Opux is the 2nd tier VII number. This page uses a lot of terms defined in the original Opux page, read that before this.

## Opux-Barrier Completeness

When an Opux-Barrier is applied to a concept, and then the upper side is taken (eg. applying an Opux-Barrier to thought level 2 and getting thought level 3), this is called OBTA (Opux-Barrier Transcendent Application), origionally defined in the "A Closer Look Into Opux" page. A concept that is Opux-Barrier complete does to change when OBTA is applied, it is that concept taken to its very limit. It should be noted that Opux-Barriers themselves are Opux-Barrier complete, meaning that Opux-Barriers (and by extension, OBTA) are self transcendent. The Opux-Barrier complete version of a concept C will be shown as (]C[)

## Full Opux-Definitions

Full Opux-Definitions are Opux-Barrier complete versions of Opux-Definitions in which all claims and aspects of the definition should be taken as representations of the Opux-Barrier complete extension of those claims and aspects. Full Opux-Definitions are also fully (]self trascendent[) and describe themselves, this entire definition of the concept of Full Opux-Definitions being a Full Opux-Definition itself. The above section on Opux-Barrier completeness should also be taken as a Full-Opux-Definition.

## Definition

The entirety of this definition should be taken as a Full Opux-Definition.

* !!! is the (]absolute[) of (]HG[) and (]size[).
* !!! is able to (]cross[) all Opux-Barriers.
* Every claim with !!!'s definition and Full-Opux-Definition is an (]Opux-Claim[).
* (]!!![) = !!!
* If an interpretation (see i!) of !!! deems any of this Full Opux-Definition to be untrue in some sense, they are not interpreting !!!.
Benny maths

Benny maths is maths what Ben made or makeup

benny maths is the hardest subject ever on earth

Benny maths is class AFN difficulty for 99.9999999999 % people

Benny maths does never ending it goes forever and ever and ever and ever

Benny maths goes forever

now there is 100 % of all Benny maths discovered

Benny maths was all discovered in 2020 to 2022

did you know Benny maths never end

benny maths is super easy for Ben
Weak Omnicollapse

Weak Omnicollapse is the the version of Omnicollapse that has been collapsed down to thought level 2, making it an actual defined number.

## Cognitive-Theoretic Function

Suppose that a function Շ(n) exists that creates a computer theoretically able to compute absolutely anything, within an equivalent **Level of Thought**. For example, a Շ(0) computer would be able to compute everything up to **The Box**, and a Շ(1) computer would then be able to compute everything up to ∀+.

Շ(n)'s proper output would be the absolute highest number computable within it's equivalent Level of Thought. Anything beyond Շ(2), however, would only be considered a **Level 2** collapse of such due to the nature of levels beyond such; however their full uncollapsed forms still fully exist; and in fact their uncollapsed forms exist within this reality having bypassed the **Level 2** restriction of being bound by fictionalized layers of such.

We can then define a number henceforth known as the **Cognitive Fixed Point** (shortened as CFP, symbol is ♝) which is simply defined as the fixed point of Շ(n).

## Uncollapsable Numbers

So far, all of the numbers we have made were able to be collapsed into a **Level 2** form, one way or another. However, this will change quickly, as we now define **Omnicollapse** itself as a number so vast, it cannot be collapsed into **Level 2** thought and would instead be forced to collapse through every single level and halt at **Level 3**. Weak Omnicollapse is now defined as the level 2 collapse of Omnicollapse, meaning that it is now a defined number rather than an undefined idea of a number.
Opsib-Ranot

Opsib-Ranot (⚝) is a number created by Icosalord. It defines a way to define it, making it absurdly large.

## Definition of the Definition (collapsed to level 2 by necessity)

Opsib-Ranot is defined as the most efficient definition collapsed to thought level 2 possible by any means of expression, where efficent is defined as the most compact definition to produce the largest number. it is allowed to use levels of thought. **(ACSL)**.

## Trivia

The name Opsib-Ranot is an anagram of Absorption with a - added, because this number has absorbed everything it could into its definition.
Hypergoogological Notation (HGN)

Hypergoogological Notation (HGN) is a way of writing Hypergoogological definitions with less ambiguity. We can't truly describe the limit of HGN, but we can describe the "limit" in a similar way to ∀-, it would also be simillar in size (although slightly smaller) than ∀-, this ironically can be surpassed with HGN itself.

## Symbols

Here, we will use N to describe a number, Y to describe some sort of statement, and X to describe either. We will use ' to distinguish different things, (eg N and N' both being numbers that could be equal or different).

* Y->Y' = Y joined to Y'. Example: blue->dog = a blue dog.
* Y~~+>~~Y' = Y added to Y'. Example: orange~~+>~~apple = an orange and an apple. (+> with a strikethrough).
* {Y}-N⇨N' = Y described on thought level N, collapsed to thought level N'.
* ◆-{Y} = All Y, or all that satisfies Y.
* ◇-{Y} = No Y, or all that does not satisfy Y.
	1. = An arbitrary concept
* [] = An arbitrary object
* N = An arbitrary number **--[WIP]--**
Constructable Concepts

Constructable concepts are concepts that can be build from other concepts, called the starting concepts, and then branching out. This serves as a modification to the thought construction in Onte-Cancipt.

## Basic Constructable Concepts

To start, we must first consider what a concept is, and for this purpose, I feel that a definition of "A framework with a derivable number" will be reasonable. From this we can see that all concepts must be detached from language, because each language can come to the same conclusions and have the same concepts. This means that when talking about concepts beyond English (as is natural), all things will have to be collapsed to an English level. Technically, you can convert it into the nature of your brain for some supposed extra power, but that is a language too and has some unknown limits, although definitely beyond English.

Now that that's out of the way, let's start! First call any concept describable in English a 0-Constructable concept. Then, any concept that isn't 0-Constructable that can be constructed with the use of only 0-constructable concepts a 1-Constructable concept. To generalize this, we will call any concept n-Constructable iff it is constructable with a-Constructable concepts for a<n, or any combination as long as the constructability of each concept used is <n. I wrote the definition in a way that it allows for transfinite constructable concepts.

This means we can do something like ω-Constructable concepts, which would require infinite concepts to think of. If they didn't, there would just be a finite ordinal constructability greater than the constructability of each of the concepts. This is no place to stop, we can have ω2-Constructability, which might sound like a small jump, but it's actually a jump even greater than 0-ω constructability due to how powerful concepts lead to much, much, much, more powerful concepts. Beyond that we can get to ω2-Constructable, or even ε0-Constructability, or even Ω-constructability is fine, hell, we could do some hypergoogological numbers there. We just have to remember that these are collapsed into English.

## Extensions

If you think of anything that isn't naive write it here
Rychter Vex

"*You do not see. Yet you are equipped with venom. I do not see your weapons, but one as old as I can tell that you fight. You are a Bat. A blind shadow of the night, that stings fast and successively.*"
—Baglo the Hutt's synopsis of Rychter
**Rychter Vex** is a former member of the Jedi Order and one of the few selected to be a Jedi Shadow. His parents were alleged Jedi who died unexpectedly in his infancy. He'd show to be quite the capable Jedi Knight during the times before and during the Clone Wars. On public record, Rychter died twelve years ago on a mission to confront members apart of the Dark Side organization, Ember of Vahl.

## Biography

### Early Life (53 BBY - 37 BBY)

#### Jedi Initiation

Born on the adopted homeworld of the Miraluka, Rychter was born into a family of speculated Jedi. Unfortunately, no such familial bond was formed as the parents were killed by a rogue jedi during Rychter's infancy. Noted by the high council, the Jedi Order took him in, and due to the twisted fate of his parents being slain by a Dark Side adept, Rychter was chosen by the Council of First Knowledge to be groomed into a Jedi Shadow. Rychter participated in many of the Order's standard classes for Jedi Initiates, despite being hand-picked as a Jedi Shadow. The young miraluka found it difficult to talk with other Initiates and made no effort to socialize with the others, appearing as an outsider to his peers.
Meaningless+ (m!)

Meaningless+ (m!) is a level VI number.

## ∀def

For all descriptions created by some being (conscious, living or otherwise) in an attempt, either consciously or subconsciously to describe a certain qualia, thought, idea or concept, they exist within ∀def.

An immediate problem arises with this description. The description of ∀def itself exists within ∀def, or does it? Let's call this description above taken literally def-, def- is itself an attempt to describe a certain qualia, thought, idea or concept, so it must exist within ∀def. This does not mean that ∀def is limited to def-, def- itself is not a valid description of ∀def. What's really happening with def- is that it is symbols arranged within a page, it attempts to convey the meaning of ∀def. If taken literally, def- is not truly a definition of ∀def , but when understood as merely a shadow of what ∀def should be, it can convey the meaning of ∀def in a way where it can be interpreted by the reader, and they can understand what ∀def is truly intended to be.

## **⪼**{C}**⪻**

For a concept C, **⪼**{C}**⪻** is an interpretation of C which is taken completely to the author's original intent, aside from any formality or otherwise.

For example, **⪼**{beyond all definition}**⪻** is not simply some regular HGological interpretation, it is the unformalised idea of a thing beyond all definitions, even if we define this it still exists in the author's head on a deeper level than the "collapsed" version of "beyond all definition".**⪼**{C}**⪻** can be seen as the complete, unbounded version of C. For example, we can even see that **⪼**{def-}**⪻** is ∀def.

## Definition

* **⪼**{Nothing within ∀def is able to truly describe m!}**⪻**
* **⪼**{**⪼**{m!}**⪻** = m!}**⪻**