BusyBeaverWiki - User contributions [en]

Cryptids

2024-11-17T03:13:40Z

Lengyijun: Verified in https://github.com/lengyijun/goldbach_tm/

'''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 mathematically-hard.

If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.

The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html blog post] announcing the discovery of [[Bigfoot]].

== Cryptids at the Edge ==

This is a list of Minimal Cryptids (Cryptids in a class with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|[[Bigfoot]]
|[[BB(3,3)]]
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|[https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard]
|Nov 2023
|[[User:Sligocki|Shawn Ligocki]]
|
|-
|[[Hydra]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard]
|May 2024
|Daniel Yuan
|
|-
|
|BB(2,5)
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB1LB|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid]
|May 2024
|Daniel Yuan
|
|-
|[[Antihydra]]
|[[BB(6)]]
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|[https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318 Discord message]
|June 2024
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|}

== Larger Cryptids ==

A more complete list of all known Cryptids over a wider range of states and symbols. These Cryptds were all "constructed" rather than "discovered".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|ZF
|BB(745)
|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
|
|2016, 2023
|O’Rear and Riebel
|The machine halts if and only if [[wikipedia:Zermelo–Fraenkel_set_theory|Zermelo–Fraenkel set theory]] is inconsistent.
|-
|RH
|BB(744)
|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|
|2016
|Matiyasevich and O’Rear
|The machine halts if and only if [https://en.wikipedia.org/wiki/Riemann_hypothesis Riemann Hypothesis] is false.
|-
|Goldbach
|BB(25)
|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6<nowiki/>
|
|2016
|anonymous
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false. Its behavior has been verified in Lean.<ref>https://github.com/lengyijun/goldbach_tm</ref>
|-
| Erdős || BB(5,4) and
BB(15)
|
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt

https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|-
|Weak Collatz
|BB(124) and BB(43,4)
|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
|
|Jul 2021
|[[User:Cosmo|Tristan Stérin]]
|The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.
Not independently verified, and probably easy to further optimise.
|-
| Bigfoot - compiled|| [[BB(7)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
|-
| Hydra - compiled
|BB(9)
|<pre>
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
</pre>[[File:Hydra_9_states.txt]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1251572501578780782 Discord message]
|June 2024
|<code>@Iijil1</code>
|Compilation of Hydra into 2 symbols, all[https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].
|}

== Beeping Busy Beaver ==

Cryptids were actually noticed in the [[Beeping Busy Beaver]] problem before they were in the classic Busy Beaver. See [[Mother of Giants]] describing a "family" of Turing machines which "[[probviously]]" [[quasihalt]], but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in <code>1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA</code> with different values.

Cryptids

2024-11-16T05:05:29Z

Lengyijun: Actually, it's a 26-state Turing machine : 22 and 24 are same state. Verified in https://github.com/lengyijun/goldbach_tm

'''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 mathematically-hard.

If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.

The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html blog post] announcing the discovery of [[Bigfoot]].

== Cryptids at the Edge ==

This is a list of Minimal Cryptids (Cryptids in a class with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|[[Bigfoot]]
|[[BB(3,3)]]
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|[https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard]
|Nov 2023
|[[User:Sligocki|Shawn Ligocki]]
|
|-
|[[Hydra]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard]
|May 2024
|Daniel Yuan
|
|-
|
|BB(2,5)
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB1LB|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid]
|May 2024
|Daniel Yuan
|
|-
|[[Antihydra]]
|[[BB(6)]]
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|[https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318 Discord message]
|June 2024
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|}

== Larger Cryptids ==

A more complete list of all known Cryptids over a wider range of states and symbols. These Cryptds were all "constructed" rather than "discovered".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|ZF
|BB(745)
|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
|
|2016, 2023
|O’Rear and Riebel
|The machine halts if and only if [[wikipedia:Zermelo–Fraenkel_set_theory|Zermelo–Fraenkel set theory]] is inconsistent.
|-
|RH
|BB(744)
|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|
|2016
|Matiyasevich and O’Rear
|The machine halts if and only if [https://en.wikipedia.org/wiki/Riemann_hypothesis Riemann Hypothesis] is false.
|-
|Goldbach
|BB(26)
|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6<nowiki/>
|
|2016
|anonymous
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false. Its behavior has been verified in Lean.<ref>https://github.com/lengyijun/goldbach_tm</ref>
|-
| Erdős || BB(5,4) and
BB(15)
|
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt

https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|-
|Weak Collatz
|BB(124) and BB(43,4)
|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
|
|Jul 2021
|[[User:Cosmo|Tristan Stérin]]
|The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.
Not independently verified, and probably easy to further optimise.
|-
| Bigfoot - compiled|| [[BB(7)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
|-
| Hydra - compiled
|BB(9)
|<pre>
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
</pre>[[File:Hydra_9_states.txt]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1251572501578780782 Discord message]
|June 2024
|<code>@Iijil1</code>
|Compilation of Hydra into 2 symbols, all[https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].
|}

== Beeping Busy Beaver ==

Cryptids were actually noticed in the [[Beeping Busy Beaver]] problem before they were in the classic Busy Beaver. See [[Mother of Giants]] describing a "family" of Turing machines which "[[probviously]]" [[quasihalt]], but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in <code>1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA</code> with different values.

Cryptids

2024-11-10T00:32:57Z

Lengyijun: I have verified yet : https://github.com/lengyijun/goldbach_tm

'''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 mathematically-hard.

If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.

The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html blog post] announcing the discovery of [[Bigfoot]].

== Cryptids at the Edge ==

This is a list of Minimal Cryptids (Cryptids in a class with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|[[Bigfoot]]
|[[BB(3,3)]]
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|[https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard]
|Nov 2023
|[[User:Sligocki|Shawn Ligocki]]
|
|-
|[[Hydra]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard]
|May 2024
|Daniel Yuan
|
|-
|
|BB(2,5)
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB1LB|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid]
|May 2024
|Daniel Yuan
|
|-
|[[Antihydra]]
|[[BB(6)]]
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|[https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318 Discord message]
|June 2024
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|}

== Larger Cryptids ==

A more complete list of all known Cryptids over a wider range of states and symbols. These Cryptds were all "constructed" rather than "discovered".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|ZF
|BB(745)
|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
|
|2016, 2023
|O’Rear and Riebel
|The machine halts if and only if [[wikipedia:Zermelo–Fraenkel_set_theory|Zermelo–Fraenkel set theory]] is inconsistent.
|-
|RH
|BB(744)
|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|
|2016
|Matiyasevich and O’Rear
|The machine halts if and only if [https://en.wikipedia.org/wiki/Riemann_hypothesis Riemann Hypothesis] is false.
|-
|Goldbach
|BB(27)
|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6<nowiki/>
|
|2016
|anonymous
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false.
|-
| Erdős || BB(5,4) and
BB(15)
|
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt

https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|-
|Weak Collatz
|BB(124) and BB(43,4)
|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
|
|Jul 2021
|[[User:Cosmo|Tristan Stérin]]
|The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.
Not independently verified, and probably easy to further optimise.
|-
| Bigfoot - compiled|| [[BB(7)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
|-
| Hydra - compiled
|BB(9)
|<pre>
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
</pre>[[File:Hydra_9_states.txt]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1251572501578780782 Discord message]
|June 2024
|<code>@Iijil1</code>
|Compilation of Hydra into 2 symbols, all[https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].
|}

== Beeping Busy Beaver ==

Cryptids were actually noticed in the [[Beeping Busy Beaver]] problem before they were in the classic Busy Beaver. See [[Mother of Giants]] describing a "family" of Turing machines which "[[probviously]]" [[quasihalt]], but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in <code>1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA</code> with different values.

Cryptids

2024-11-10T00:31:00Z

Lengyijun: I have verified yet : https://github.com/lengyijun/goldbach_tm

'''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 mathematically-hard.

If there exists a Cryptid with n states and m symbols, then BB(n, m) cannot be solved without solving this hard math problem.

The name Cryptid was proposed by Shawn Ligocki in an Oct 2023 [https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html blog post] announcing the discovery of [[Bigfoot]].

== Cryptids at the Edge ==

This is a list of Minimal Cryptids (Cryptids in a class with no strictly smaller known Cryptid). All of these Cryptids were "discovered in the wild" rather than "constructed".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|[[Bigfoot]]
|[[BB(3,3)]]
|{{TM|1RB2RA1LC_2LC1RB2RB_---2LA1LA|undecided}}
|[https://www.sligocki.com/2023/10/16/bb-3-3-is-hard.html BB(3, 3) is hard]
|Nov 2023
|[[User:Sligocki|Shawn Ligocki]]
|
|-
|[[Hydra]]
|[[BB(2,5)]]
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB0LA|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html BB(2, 5) is hard]
|May 2024
|Daniel Yuan
|
|-
|
|BB(2,5)
|{{TM|1RB3RB---3LA1RA_2LA3RA4LB0LB1LB|undecided}}
|[https://www.sligocki.com/2024/05/10/bb-2-5-is-hard.html#a-bonus-cryptid A Bonus Cryptid]
|May 2024
|Daniel Yuan
|
|-
|[[Antihydra]]
|[[BB(6)]]
|{{TM|1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA|undecided}}
|[https://discord.com/channels/960643023006490684/1026577255754903572/1256223215206924318 Discord message]
|June 2024
|<code>@mxdys</code>, shown to be a Cryptid by <code>@racheline</code>.
|Same as '''Hydra''' but starting iteration from 8 instead of 3 and with termination condition <code>O > 2E</code> instead of <code>E > 2O</code>, hence the name '''Antihydra'''.
|}

== Larger Cryptids ==

A more complete list of all known Cryptids over a wider range of states and symbols. These Cryptds were all "constructed" rather than "discovered".

{| class="wikitable"
|-
! Name !! BB domain !! Machine !! Announcement !! Date !! Discoverer !! Note
|-
|ZF
|BB(745)
|O'Rear's machine: https://github.com/sorear/metamath-turing-machines/blob/master/zf2.nql
Riebel's analysis: https://www.ingo-blechschmidt.eu/assets/bachelor-thesis-undecidability-bb748.pdf
|
|2016, 2023
|O’Rear and Riebel
|The machine halts if and only if [[wikipedia:Zermelo–Fraenkel_set_theory|Zermelo–Fraenkel set theory]] is inconsistent.
|-
|RH
|BB(744)
|https://github.com/sorear/metamath-turing-machines/blob/master/riemann-matiyasevich-aaronson.nql
|
|2016
|Matiyasevich and O’Rear
|The machine halts if and only if [https://en.wikipedia.org/wiki/Riemann_hypothesis Riemann Hypothesis] is false.
|-
|Goldbach
|BB(27)
|https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6<nowiki/>(unverified)
|
|2016
|anonymous
|The machine halts if and only if [https://en.wikipedia.org/wiki/Goldbach%27s_conjecture Golbach's conjecture] is false.
|-
| Erdős || BB(5,4) and
BB(15)
|
https://docs.bbchallenge.org/other/powers_of_two_5_4.txt

https://docs.bbchallenge.org/other/powers_of_two_15_2.txt
|| [https://arxiv.org/abs/2107.12475 arxiv preprint] || Jul 2021 || [[User:Cosmo|Tristan Stérin]] (<code>@cosmo</code>) and Damien Woods || The machine halts if and only if the following conjecture by Erdős is false: "For all n > 8, there is at least one 2 in the base-3 representation of 2^n"
|-
|Weak Collatz
|BB(124) and BB(43,4)
|https://docs.bbchallenge.org/other/weak_Collatz_conjecture_124_2.txt (unverified)
https://docs.bbchallenge.org/other/weak_Collatz_conjecture_43_4.txt (unverified)
|
|Jul 2021
|[[User:Cosmo|Tristan Stérin]]
|The machine halts if and only if the "weak Collatz conjecture" is false. The weak Collatz conjecture states that the iterated Collatz map (3x+1) has only one cycle on the positive integers.
Not independently verified, and probably easy to further optimise.
|-
| Bigfoot - compiled|| [[BB(7)]]|| <code>0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB</code>|| [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-2140887228 Bigfoot Comment] || June 2024 || <code>@Iijil1</code>|| Compilation of Bigfoot into 2 symbols, there was a previous compilation [https://github.com/sligocki/sligocki.github.io/issues/8#issuecomment-1774200442 with 8 states]
|-
| Hydra - compiled
|BB(9)
|<pre>
0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ
</pre>[[File:Hydra_9_states.txt]]
|[https://discord.com/channels/960643023006490684/1084047886494470185/1251572501578780782 Discord message]
|June 2024
|<code>@Iijil1</code>
|Compilation of Hydra into 2 symbols, all[https://discord.com/channels/960643023006490684/1084047886494470185/1253193750486974464 confirmed by Shawn Ligocki]. <code>@Iijil1</code> provided 24 TMs which all emulate the same behavior.
[https://discord.com/channels/960643023006490684/1084047886494470185/1247560072427474955 Previous compilation had 10 states], by Daniel Yuan, also [https://discord.com/channels/960643023006490684/1084047886494470185/1247579473042346136 confirmed by Shawn Ligocki].
|}

== Beeping Busy Beaver ==

Cryptids were actually noticed in the [[Beeping Busy Beaver]] problem before they were in the classic Busy Beaver. See [[Mother of Giants]] describing a "family" of Turing machines which "[[probviously]]" [[quasihalt]], but requires solving a Collatz-like problem in order to actually prove it. They are all TMs formed by filling in the missing transition in <code>1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA</code> with different values.