User blog:Syst3ms/Bismuth : not Y sequence, but close

Bismuth.
I'm back with some more Y sequence stuff. This project started out as a legit algorithm for Y sequence ; it got really far, but then I started stumbling upon expansions, given by Yukito himself, which I couldn't understand. Even when getting a proper explanation, they still felt irregular and inconsistent to me. Thus, I kept my then current algorithm and ironed out all the kinks (I could find). And that's how Bismuth was born.

Y sequence was created by Yukito.



Installation and usage
The program can be simply downloaded right here.

The downloaded ZIP file contains the .jar file, as well as a .bat file (Windows) and a .sh file (for UNIX-based OS) to execute it.

Once ran, the program will simply ask you to input a sequence and once that's done it'll give you back the answer very quickly.

The source code is available here. I really couldn't be bothered with making something that works online, but if someone wants to do it, feel free to use the source like you please and make something of the sort. I'll include it in the post if that ever gets made.

If you find any bugs (most likely a big error message or an expansion that seems very wrong), please report them to me and I will get them fixed as soon as possible.

Relation to Y sequence
As previously mentioned, Bismuth diverges from Y sequence at some point. If I recall correctly, the first sequence that expands differently is (1,3,4,2,5,6,5). However, please note that Y sequence not having been formalized (yet) or gotten an agreed-upon definition (yet), these expansions might change depending on Yukito's will. Furthermore, the expansions of some sequences are still an undecided open problem in Y sequence.

However it seems that throughout all expansions where the two diverge, Bismuth has always been weaker than Y sequence. I therefore believe that Bismuth cannot be stronger than Y sequence, and at most of the same strength. I also believe it follows that proving the nontermination of Bismuth would also prove the nontermination of Y sequence as a whole, which, if the faulty sequence sits below (1,3), theorized limit of BMS, could also solve the question of its termination. But this last conclusion is not specific to Bismuth and can also be applied to Y sequence.

Now that this project is mostly closed, I'll fall back to attempts to extend STON a third and last time. However, this is still all I have for today.