Launch BMS MCP server
I made a MCP server for expansion of BMSv4.
MCP server is an interface of LLM(Claude, cline and so on.)
How to setup: https://github.com/koteitan/yaBMS/tree/master/mcp
Your LLM will be able to use BMS expansions.
The server name is "yabms", and the command name is "expand_bms".
A history of Repeating Mazes
I created a large number system called User Blog:Koteitan/Pentation Maze, and as a special feature, I will introduce an endless collection of repeating mazes that I came across during my research.
- 1 Fractal Mazes
- 1.1 FRACTAL MAZE
- 2 Conclusion
- 3 Future Considerations
In 1999, Mark J. P. Wolf introduced a recursive maze called FRACTAL MAZE in the magazine Extropy.
As a result, I attempted to show that the maximum depth of the shallowest solution in a fractal block maze with a reduction ratio of 1/N is at most \(8N(8N-1)/2=32N^2-4\), but there are still unresolved issues.
As we have seen above, the complexity of fractal mazes is limited, with the shallowest solution's depth being at most \(8N(8N-1)/2\), meaning it does not exceed the order of \(N^2\).
This s…
Pentation Maze
I created something called a “pentation maze.”
Within the colored blocks on the left, there is a winding passageway as shown on the right. Many different types of blocks are arranged in a regular pattern. Below is a link to a video showing how this maze is played:
Additionally, you can explore this maze on a dedicated website, just as shown above.
t this point, I remembered a project I had worked on when reading about thePyramid Maze--a structure I called the Collatz Maze.
Collatz Maze - External Link
This maze consists of three types of blocks:
- thru: Connects top to bottom and left to right.
- odd: Connects left and right to the top.
- even: Connects left and right to the bottom.
Along the line \(y=x\) odd and even blocks are alternately arranged. Whe…
Pentation Calculation by Generalized Collatz System
\(\newcommand{\penta}{ {\mathrm {penta}}}\) \(\newcommand{\tif}{ {\mathrm {if}}~}\) \(\newcommand{\else}{ {\mathrm {else}}~}\) \(\newcommand{\then}{ {\mathrm {then}}~}\) \(\newcommand{\otherwise}{ {\mathrm {otherwise}}~}\) \(\renewcommand{\mod}{ {\mathrm {mod}}~}\) I made Pentation calculation formula using recurrence relations by residue classes, as commonly seen in Generalized Collatz Problem.
- 1 Definition
- 2 Theorem
- 3 Haskell code
- 4 References
I defined a function from a natural number to a natural number as follows: \begin{eqnarray} &&\begin{array}{lllllllll} &\tif x \not \equiv 0 (\mod 2) &\land& x \not \equiv 0 (\mod 5)& & & \then & \penta(x) &=& x ,&\else \\ &\tif x \not \equiv 0 …
Hydra Diagram for Multiple Variable Extended Buchholz's Psi and the expansion rule
\( \newcommand{\bm}[1]{\boldsymbol #1} \newcommand{\len}{ {\rm len}} \newcommand{\if}{~{\rm if}~} \newcommand{\nat}{ {\mathbb N} } \)
I update Multiple Variable Extended Buchholz Hydra, which is the hydra notation corresponding to Multiple Variable Extended Buchholz's psi. I also defined the expansion rule and the large number by it.
- 1 Extended Buchholz's OCFs and functions
- 1.1 notation
- 1.2 order
- 1.3 expansion
- 2 Large number
- 3 References
There are some ordinal-collapsing functions and notations made as extensions of Buchholz's ψ function
I define the expansion rule for MVEBH v3.1 as follows by pair sequences. The symmetric notation simplified the expansion rules.
I define a set of pair sequence \(T\) as follows. The following \(a\) and \(b\) are natural n…