The Crystallization of Googology Wiki

I made this series to revive Redstonepillager's "Googology Wiki 15th anniversary special series" in a different way, as the series has been abandoned and deleted with reason "deleting the series after Christmas 2023 because the last few numbers of the series should be legitimately added until the Christmas Day in order to finalize the entire series which is a pure joke and is completely insincere, as well as numerous issues; however, the numbers will be kept and transferred to another page".

This is also known as "New Year numbers 2024", a successor to Meet youself in 105 degrees Celsius, and it's inspired by ARsygo's The 15 is here.

The Crystallization of Googology Wiki is a series of 50 numbers defined by googology wiki user HaydenTheGoogologist2009. Please note that not all numbers are well-defined.

The reason why this series is called The "Crystallization" of Googology Wiki is because the 15th wedding anniversary is also known as the "crystal" anniversary.

Notes

1. Most of these numbers are either using a foreign language or long sentences.

2. There won't be too many ill-defined numbers in this series. But even if they're ill-defined, they must be an extension of a notable notation that's included in the list of notations in the analyses section of the policy.

3. None of the names of the numbers are used to spread false statements, bothering actual people, spreading the false terminology, etc.

4. Unless otherwise specified, all BMS expressions are with respect to version 2.3 = 4, simulating Hardy Hierarchy.

5. All of the numbers are based off of number 15 and the multiples of 15 (30, 45, 60, 75, 90, etc.).

List of numbers

1. Rin = 1.5 * 10^1515

2. Ruri = 15^^^^15

3. Hayate = G1500 in Graham sequence

4. Sumire = A(15, 15) in Ackermann function (Robinson's definition)

5. Koei = 15vvvvvvvvvvvvvvv30 in Down-arrow notation

6. Haydenese number = {100, 100, 2, 3} in BEAF

7. Seiko = {15, 15 (1) 15, 15 (1) 15, 15 (1) 15, 15 (1) 15, 15} in BEAF

8. Kosai = {15, 15 (45, 44, 43, ..., 3, 2, 1) 2} in BEAF

9. Moegi = {15, 15 (1(1(1(1(1)1)1)1)1) 2} in BEAF

10. Gekka = {X, X (X^2 + 7X + 10) X} & 15 using the array of operator and BEAF

11. Awayuki = {15, 15 [1 [60 ¬ 75] 2] 2} in BAN

12. Gyoten = {15, 15 [1 [2 \_{90} 2]_{1} 2] 2} in BAN

13. Shinonome = {15, 15 [1 [2 \_{1 \_{105} 2} 2] 2] 2} in D. Shamlin Jr's extension of BAN

14. Ginrei = E[15]15#^(120)15#^(119)15#^(118)15 ... ###15##15#15 in Extended Hyper-E notation

15. Horaku = E[15]15#^^^^^###>#^^^^^###15 in Extended Cascading-E Notation

16. Enraku = E[15]15#{135}#15#15#15 in Hyper-Extended Cascading-E Notation

17. Yuen = E[15]15#{&^&^&^&^&}#15 in Collapsing-E Notation

18. Kyoen = E[15]15#{&_{150}}#15 in Extended Collapsing-E Notation

19. Ooh! Did you get detention? What did you do? = 3 -> 4 -> 5 -> ... -> 175,000 -> ... -> 4 -> 3 -> 2 in Chained arrow notation

20. You look kinda familiar. Did I see you before? = 190 ->_{220} 205 in Peter Hurford's extension of chained arrows

21. Report him! He’s bullying me! = Concentration of 1[235] and 9[250] = 111...111999...999 with 235 1's and 250 9's in Copy notation

22. Wanna try my secret recipe? = 265[1 {1 \ 1 {1 \ 2} 2} 2]265 in DeepLineMadom's Array Notation

23. This guy is literally crazy. = 280[1 {1 \ 1 {1 \ 2 \ 2} 2 \ 1, 2} 2]280 in DeepLineMadom's Array Notation

24. He’s my boss, not yours! = [295, 295, 295, [295, 295, 295, [295, 295, 295, 295]] in Graham Array Notation

25. Wait, you’re in the competition too? = (310!295) / (265!235 * 280!265 * 295!280) in Hyperfactorial array notation

26. What, why can’t you eat that? = 325![1, 2, 3, ..., 12, 1, 2, 3, ..., 12] in Hyperfactorial array notation

27. ⠀ (Braille pattern blank, U+2800) = 340![1(1)1(1)1(1)1]/w355 in Hyperfactorial array notation

28. This guy, the top student in the school, he is. = H*(10^10^10^10^(10^370 + 13))

29. This guy, the master of everything. = 5[5[5[... 5[5[5]] ...]]] (385 5's) in Steinhaus-Moser Notation

30. This guy is really pitiful. = 400{X^4 + 6X^3 + X^2 + 10X + 147}400 in X-Sequence Hyper-Exponential Notation

31. You don’t have to pay attention to him. He’s crazy. = A(1, 1, 1, 1, 1, 1, 0, 0, 0) in Taro's multivariable Ackermann function

32. Aren’t you the person who I met yesterday? = (0, 0)(1, 1)(1, 1)(1, 1)(2, 2)[415] in Bashicu matrix system

33. Guys, stop whining and be positive! = (0, 0, 0)(1, 1, 1)(2, 2, 2) ... (100, 100, 100)[430] in Bashicu matrix system

34. All students, line up. Now! = s(445, 445 {460 ````` 459 ````` 458 ````` ... ````` 3 ````` 2 ````` 1 ````` 2 ````` 3 ````` ... ````` 458 ````` 459 ````` 460 ```` 459 ```` 458 ```` ... ```` 3 ```` 2 ```` 1 ```` 2 ```` 3 ```` ... 458 ```` 459 ```` 460 ``` 459 ``` 458 ``` ... ``` 3 ``` 2 ``` 1 ``` 2 ``` 3 ``` ... ``` 458 ``` 459 ``` 460 `` 459 `` 458 ... ``3 `` 2 `` 1 `` 2 `` 3 `` ... `` 458 `` 459 `` 460 ` 459 ` 458 ` ... ` 3 ` 2 ` 1 ` 2 ` 3 ` ... ` 458 ` 459 ` 460} 2) in Strong array notation

35. Hi! Did anyone miss me? = s(475, 475 {1 {111 ,,, 111 ,,, 111 ,,, 111 ,,, 111 ,,, 111 ,,, 111 ^,,,} 2} 2) in Strong array notation

36. Ultimate regional destruction = f_{ω + 1}(262,537,412,640,768,744) in Fast-growing hierarchy

37. One toilet billion guests = H_{ψ0(Ω_ψ0(Ω_Ω))}(490) in Hardy hierarchy with this system of fundamental sequences

38. Two slices five roots = g_{ζ_5}(505) in Slow-growing hierarchy with this system of fundamental sequences

39. This is the most annoying number name ever in the history of the metaverse. = √(535^2 - 520^2) ≈ 125.7974563

40. Jing Guan Ü = 550^550^550^550^550^5.5

41. My senior brother expressed his helplessness. = log_{3}(ln(565)) ≈ 1.680645655

42. The crowd, and the champion = |sin(580)| in degrees where |...| represents the absolute value ≈ 0.642787609

43. One champion, has won all the people in the crowd. = |cos(595)| in radians ≈ 0.325752805

44. Now, he's our idol! = tan(610) in gradians ≈ 0.15838444

45. He's the superstar of the whole school. = ∛(625^3 + 640^3) ≈ 797.0120966

46. He should be superior to others. = e^π^654.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999912345678901 (654.99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999912345678901 is a terminating decimal)

47. The last page of him. See you again by fate! = sin-1(1/670) in degrees ≈ 0.095017911

48. You will be remembered in our hearts forever! = cos-1(1/685) in radians ≈ 1.569336472

49. The final. Goodbye for now! = tan-1(1/700) in gradians ≈ 0.090945619

50. Ultra Grahamese Number = 0.2425950695064738395657479136519351798334535362521430035401260267716226721604198106522631693551887803881448314065252616878509555264605107117200099709291249544378887496062882911725063001303622934916080254594614945788714278323508292421020918258967535604308699380168924988926809951016905591995119502788717830837018340236474548882222161573228010132974509273445945043433009010969280253527518332898844615089404248265018193851562535796399618993967905496638003222348723967018485186439059104575627262464195387 (decimal of the last 500 digits of G(n) of the Graham sequence) (terminating decimal)