Cryptids are Turing Machines whose behavior (when started on a blank tape) can be described completely by a relatively simple mathematical rule, but where that rule falls into a class of unsolved (and presumed hard) mathematical problems. This definition is somewhat subjective (What counts as a simple rule? What counts as a hard problem?). In practice, most currently known small Cryptids have Collatz-like behavior. In other words, the halting problem from blank tape of cryptids is mathematica...| wiki.bbchallenge.org
Note: All Discord links are for the https://bbchallenge.org/ Discord server.| sligocki
BB(5) = 47,176,870 We are extremely happy to announce that, after two years of intense collaboration, the goal of the Busy Beaver Challenge has been reached: the conjecture “BB(5) = 47,176,870” is proved. Exceeding our expectations, the proof has been formally written in Coq by collaborator mxdys whose work improves on and/or uses the contributions of more than 10 other bbchallenge contributors (see credits). The formal theorem’s statement was reviewed by independent Coq experts (see cr...| The Busy Beaver Challenge
Consider the Collatz-like function:| sligocki
I’m excited to share a 3 state, 3 symbol Turing Machine that cannot be proven to halt or not (when starting on a blank tape) without solving a Collatz-like problem. Therefore, solving the \(BB(3, 3)\) problem is at least as hard as solving this Collatz-like problem, a class of problem for which Paul Erdős famously said: “Mathematics may not be ready for such problems.”| sligocki