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Large Number Lying on the Boundary of the Rule of Touhou Large Number 4 (Japanese: 東方巨大数4の規則の境界を突いた巨大数) is a large number submitted to a Japanese large number contest.[1] The term was coined by 巨大数大好きbot on 28/07/2021.

八雲語

巨大数大好きbot invented 八雲語, which is a mathematical language similar to an assembly language, to describe the definition. Let \(K\) denote the set of alphabets given as 常用漢字, i.e. kanjis in Japanese standard level, and \(F\) denote the set of all maps of type \(K \to (\mathbb{Z}^2 \to \mathbb{Z})\). 八雲語 is formulated so that each sentence describes a map of type \(F \to F\).

Although 八雲語 is a language imitating an assembly language[note 1], it is formulated as a partial map from the set \(S\) of formal strings consisting of one or more Unicode letters to the set of all maps of type \(F \to F\).

Roughly speaking, elements of \(K\) correspond to a name of a variable for a two dimensional array, elements of \(F\) correspond to data in the memory, elements of \(S\) correspond to formal strings expressing commands, and "partial maps from \(S\) to the set of all maps of type \(F \to F\)" correspond to sets of commands.

Definition

Let \(z \in F\) denote the lambda expression λk. (λx,y. 0), and define 東方巨大数4の規則の境界を突いた巨大数 as the resulting value of the estimation of the following function written in 八雲語:

繝リ龍繝ン繝セ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン縺ス縺ォ繧ョ縺ェ哀縺ャ繝セ龍繝ァ哀繧ァ繝ッ繧ァ繝ヲ繝ィ哀繧ァ繝ッ繧ァ繝ヲ繝ォ哀繧ァ繝ッ繧ァ繝ヲ繝ン縺ン繝セ高繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン繝セ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン繝セ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ョ繝ン縺カ切縺ァ繧ァ縺ィ繧ァ縺ォ繧ィ縺ャ縺ナ切縺ァ繧ァ縺ィ繧ィ縺ォ繧ィ縺ャ繝セ龍繝ァ切繧ァ繝ッ繧ァ繝ヲ繝ィ切繧ァ繝ッ繧ィ繝ヲ繝ォ繧ァ繝ン繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン縺ラ典縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン縺ン繝イ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン縺ュ繝セ悪繝ァ繧ァ繝ィ繧ァ繝ォ切繧ァ繝ッ繧ァ繝ヲ繝ン繝セ悪繝ァ繧ァ繝ィ繧ィ繝ォ切繧ァ繝ッ繧ィ繝ヲ繝ン繝セ差繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン縺イ差縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ繝イ悪繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン繝セ根繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン縺ラ根縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ繝イ悪繝ァ繧ァ繝ィ繧ァ繝ォ繧ヲ繧ィ繝ン繝セ根繝ァ繧ァ繝ィ繧ァ繝ォ龍悪繧ァ繝ッ繧ァ繝ヲ繝ッ悪繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン縺ン繝サ差繝ァ繧ァ繝ィ繧ァ繝ホ龍繝ァ悪繧ァ繝ッ繧ァ繝ヲ繝ィ悪繧ァ繝ッ繧ィ繝ヲ繝ホ根繝ァ繧ァ繝ィ繧ァ繝ン縺ン繝サ移繝ァ繧ァ繝ィ繧ァ繝ホ切繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ァ繝ン繝サ移繝ァ繧ァ繝ィ繧ィ繝ホ切繝ァ繧ァ繝ィ繧ィ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ン縺タ差縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ繝イ移繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン縺ン繝サ写繝ァ繧ァ繝ィ繧ィ繝ホ高繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ン繝セ昇繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン繝ア向繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ァ繝ン縺サ縺ォ底繧ァ繝ッ繧ァ繝ヲ縺ャ縺サ縺ォ移繧ァ繝ッ繧ァ繝ヲ縺ャ繝サ泉繝ァ繧ァ繝ィ繧ァ繝ホ向繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ァ繝ン繝ア向繝ァ繧ァ繝ィ繧ィ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン繝ア向繝ァ繧ァ繝ィ繧ィ繝ホ向繝ァ繧ァ繝ィ繧ィ繝ホ昇繝ァ繧ァ繝ィ繧ァ繝ン縺サ縺ォ写繧ァ繝ッ繧ィ繝ヲ縺ャ繝サ泉繝ァ繧ァ繝ィ繧ィ繝ホ向繝ァ繧ァ繝ィ繧ィ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン繝コ龍繝ァ向繧ァ繝ッ繧ァ繝ヲ繝ィ向繧ァ繝ッ繧ィ繝ヲ繝ホ龍繝ァ泉繧ァ繝ッ繧ァ繝ヲ繝ィ泉繧ァ繝ッ繧ィ繝ヲ繝ン繝イ向繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン縺ン繝イ向繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン繝イ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン縺ン繝ア高繝ァ繧ァ繝ィ繧ァ繝ホ高繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン繝ア昇繝ァ繧ァ繝ィ繧ァ繝ホ昇繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン縺ン繝イ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ヲ繧ィ繝ン繝セ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ァ繝ン繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン縺ラ典縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン縺ン繝イ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン縺ン縺ン繝セ龍繝ァ切繧ァ繝ッ繧ァ繝ヲ繝ィ切繧ァ繝ッ繧ィ繝ヲ繝ォ繧ァ繝ン繝イ底繝ァ繝ィ繧ァ繝ォ繧ァ繝ン(z)(底)(0,0)

Refactoring

Since the original definition above is difficult to read, the creator wrote a code inserting new lines, blank lines, and indents to it so that it becomes easier to read (except for the portion (z)(底)(0,0)) right after the description of it.

繝リ龍繝ン
繝セ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン
縺ス縺ォ繧ョ縺ェ哀縺ャ
    繝セ龍繝ァ哀繧ァ繝ッ繧ァ繝ヲ繝ィ哀繧ァ繝ッ繧ァ繝ヲ繝ォ哀繧ァ繝ッ繧ァ繝ヲ繝ン
縺ン

繝セ高繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン
繝セ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ョ繝ン
繝セ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ョ繝ン

縺カ切縺ァ繧ァ縺ィ繧ァ縺ォ繧ィ縺ャ
    縺ナ切縺ァ繧ァ縺ィ繧ィ縺ォ繧ィ縺ャ
        繝セ龍繝ァ切繧ァ繝ッ繧ァ繝ヲ繝ィ切繧ァ繝ッ繧ィ繝ヲ繝ォ繧ァ繝ン
        繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン
        繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン
        縺ラ典縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ
            繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン
            繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン
        縺ン
        繝イ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン
    縺ュ
        繝セ悪繝ァ繧ァ繝ィ繧ァ繝ォ切繧ァ繝ッ繧ァ繝ヲ繝ン
        繝セ悪繝ァ繧ァ繝ィ繧ィ繝ォ切繧ァ繝ッ繧ィ繝ヲ繝ン
        繝セ差繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン

        縺イ差縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ
            繝イ悪繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン
            繝セ根繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン
            縺ラ根縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ
                繝イ悪繝ァ繧ァ繝ィ繧ァ繝ォ繧ヲ繧ィ繝ン
                繝セ根繝ァ繧ァ繝ィ繧ァ繝ォ龍悪繧ァ繝ッ繧ァ繝ヲ繝ッ悪繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン
            縺ン
            繝サ差繝ァ繧ァ繝ィ繧ァ繝ホ龍繝ァ悪繧ァ繝ッ繧ァ繝ヲ繝ィ悪繧ァ繝ッ繧ィ繝ヲ繝ホ根繝ァ繧ァ繝ィ繧ァ繝ン
        縺ン

        繝サ移繝ァ繧ァ繝ィ繧ァ繝ホ切繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ァ繝ン
        繝サ移繝ァ繧ァ繝ィ繧ィ繝ホ切繝ァ繧ァ繝ィ繧ィ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ン

        縺タ差縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ
            繝イ移繝ァ繧ァ繝ィ繧ィ繝ォ繧ヲ繧ィ繝ン
        縺ン

        繝サ写繝ァ繧ァ繝ィ繧ィ繝ホ高繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ン
        繝セ昇繝ァ繧ァ繝ィ繧ァ繝ォ繧ァ繝ン
        繝ア向繝ァ繧ァ繝ィ繧ァ繝ホ悪繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ァ繝ン

        縺サ縺ォ底繧ァ繝ッ繧ァ繝ヲ縺ャ
            縺サ縺ォ移繧ァ繝ッ繧ァ繝ヲ縺ャ
                繝サ泉繝ァ繧ァ繝ィ繧ァ繝ホ向繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ァ繝ン
                繝ア向繝ァ繧ァ繝ィ繧ィ繝ホ悪繝ァ繧ァ繝ィ繧ィ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン
                繝ア向繝ァ繧ァ繝ィ繧ィ繝ホ向繝ァ繧ァ繝ィ繧ィ繝ホ昇繝ァ繧ァ繝ィ繧ァ繝ン
                縺サ縺ォ写繧ァ繝ッ繧ィ繝ヲ縺ャ
                    繝サ泉繝ァ繧ァ繝ィ繧ィ繝ホ向繝ァ繧ァ繝ィ繧ィ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン
                    繝コ龍繝ァ向繧ァ繝ッ繧ァ繝ヲ繝ィ向繧ァ繝ッ繧ィ繝ヲ繝ホ龍繝ァ泉繧ァ繝ッ繧ァ繝ヲ繝ィ泉繧ァ繝ッ繧ィ繝ヲ繝ン
                    繝イ向繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン
                縺ン
                繝イ向繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン
                繝イ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン
            縺ン
            繝ア高繝ァ繧ァ繝ィ繧ァ繝ホ高繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン
            繝ア昇繝ァ繧ァ繝ィ繧ァ繝ホ昇繝ァ繧ァ繝ィ繧ァ繝ホ移繝ァ繧ァ繝ィ繧ィ繝ン
        縺ン
        繝イ切繝ァ繧ァ繝ィ繧ァ繝ォ繧ヲ繧ィ繝ン
        繝セ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ァ繝ン
        繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン
        縺ラ典縺ァ繧ァ縺ィ繧ァ縺ォ繧ァ縺ャ
            繝イ切繝ァ繧ァ繝ィ繧ィ繝ォ繧ィ繝ン
            繝セ典繝ァ繧ァ繝ィ繧ァ繝ォ龍切繧ァ繝ッ繧ァ繝ヲ繝ッ切繧ァ繝ッ繧ィ繝ヲ繝ヲ繝ン
        縺ン
        繝イ底繝ァ繧ァ繝ィ繧ァ繝ォ繧ィ繝ン
    縺ン
縺ン

繝セ龍繝ァ切繧ァ繝ッ繧ァ繝ヲ繝ィ切繧ァ繝ッ繧ィ繝ヲ繝ォ繧ァ繝ン
繝イ底繝ァ繝ィ繧ァ繝ォ繧ァ繝ン

Footnotes

  1. More precisely, since the language admits controlling structures like an if-sentence and a for-loop, it is rather close to C language.

Sources

See also

By Aeton: Okojo numbers · N-growing hierarchy
By 新井 (Arai): Arai's \(\psi\)
By バシク (BashicuHyudora): Primitive sequence number · Pair sequence number · Bashicu matrix system 1/2/3/4
By ふぃっしゅ (Fish): Fish numbers (Fish number 1 · Fish number 2 · Fish number 3 · Fish number 4 · Fish number 5 · Fish number 6 · Fish number 7 · S map · SS map · s(n) map · m(n) map · m(m,n) map) · Bashicu matrix system 1/2/3/4 computation programmes · TR function (I0 function)
By じぇいそん (Jason): Irrational arrow notation · δOCF · δφ · ε function
By 甘露東風 (Kanrokoti): KumaKuma ψ function
By 小林銅蟲 (Kobayashi Doom): Sushi Kokuu Hen
By koteitan: Bashicu matrix system 2.3
By mrna: 段階配列表記 · 降下段階配列表記 · 多変数段階配列表記 · SSAN · S-σ
By Naruyoko Naruyo: Y sequence computation programme · ω-Y sequence computation programme
By Nayuta Ito: N primitive · Flan numbers · Large Number Lying on the Boundary of the Rule of Touhou Large Number 4
By p進大好きbot: Large Number Garden Number
By たろう (Taro): Taro's multivariable Ackermann function
By ゆきと (Yukito): Hyper primitive sequence system · Y sequence · YY sequence · Y function · ω-Y sequence
See also: Template:Googology in Asia

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