I have a question that popped in my mind about Turing Machines and the Busy Beaver function.

So, from the knowledge I have, programming languages are Turing complete, meaning they can do everything a Turing Machine can, which would mean that there is a way to translate a Turing Machine program to any Turing complete programming language, right?

Following from that, let's say we have a really simple program in any programming language that loops from 1 to 108 and do some computation inside that loop

Since the number of steps this program takes is higher than 107, does it mean it can't be translated to a 4 states 2 symbol machine, since BB(4) is 107?

How does the translation from a simple loop with N steps work?

math/preprints/The-Exponential-Time-Hypothesis-is-False-October-25-2026/paper.pdf at main · openai/math

This subreddit has a rule that disallows posting language model generated research. Of course, at the time the intent of that rule was mainly to prevent crackpot/slop posts. I'm not going to make any claims one way or the other about OpenAI's explosion of papers, but they're certainly not crackpots.

The mod team is discussing a modification of the rule; however, in the mean time as this is an important topic in CS, I'm posting this as a mod so that the community may discuss it.