Cryptids

Lovecraftian Beaver fan art made by Lauren

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 blog post announcing the discovery of Bigfoot.

Cryptids at the Edge

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

Name	BB domain	Machine	Date	Discoverer	Note
Bigfoot	BB(3,3)	1RB2RA1LC_2LC1RB2RB_---2LA1LA (bbch)	Nov 2023	Shawn Ligocki
Hydra	BB(2,5)	1RB3RB---3LA1RA_2LA3RA4LB0LB0LA (bbch)	May 2024	Daniel Yuan
Bonus cryptid	BB(2,5)	1RB3RB---3LA1RA_2LA3RA4LB0LB1LB (bbch)	May 2024	Daniel Yuan	Probviously non-halting.
Antihydra	BB(6)	1RB1RA_0LC1LE_1LD1LC_1LA0LB_1LF1RE_---0RA (bbch)	June 2024	@mxdys, shown to be a Cryptid by @racheline.	Same as Hydra but starting iteration from 8 instead of 3 and with termination condition O > 2E instead of E > 2O, hence the name Antihydra.
Lucy's Moonlight	BB(6)	1RB0RD_0RC1RE_1RD0LA_1LE1LC_1RF0LD_---0RA (bbch)	Mar 2025	Racheline	Probviously halting.
	BB(6)	1RB1RC_1LC1LE_1RA1RD_0RF0RE_1LA0LB_---1RA (bbch)	Jul 2024	mxdys	Variant of Hydra and Antihydra. Probviously non-halting.
	BB(6)	1RB1LD_1RC1RE_0LA1LB_0LD1LC_1RF0RA_---0RC (bbch)	Aug 2024	mxdys	Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
	BB(6)	1RB0LD_1RC1RF_1LA0RA_0LA0LE_1LD1LA_0RB--- (bbch)	Sep 2024	Daniel Yuan	Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
	BB(6)	1RB0LB_1LC0RE_1LA1LD_0LC---_0RB0RF_1RE1RB (bbch)	Nov 2024	Racheline	Similar random walk mechanism to Hydra, Antihydra. Probviously non-halting.
Space Needle	BB(6)	1RB1LA_1LC0RE_1LF1LD_0RB0LA_1RC1RE_---0LD (bbch)	Jan 2025	mxdys	Probviously non-halting.
	BB(6)	1RB1RA_0RC1RC_1LD0LF_0LE1LE_1RA0LB_---0LC (bbch)	Jul 2024	mxdys	Has near-identical behavior to 16 related BB(6) holdouts. Probviously halting.
	BB(6)	1RB1RE_1LC1LD_---1LA_1LB1LE_0RF0RA_1LD1RF (bbch)	Jul 2024	Racheline	Probviously halting.
	BB(6)	1RB0RE_1LC1LD_0RA0LD_1LB0LA_1RF1RA_---1LB (bbch)	Jul 2024	Racheline	Probviously halting.
	BB(6)	1RB0LC_0LC0RF_1RD1LC_0RA1LE_---0LD_1LF1LA (bbch)	Jul 2024	Racheline	Probviously halting.
	BB(6)	1RB0LC_1LC0RD_1LF1LA_1LB1RE_1RB1LE_---0LE (bbch)	Nov 2024	Racheline	Probviously halting.
	BB(6)	1RB---_0RC0RE_1RD1RF_1LE0LB_1RC0LD_1RC1RA (bbch)	Nov 2024	Racheline	Probviously halting.
	BB(6)	1RB0LD_1RC1RA_1LD0RB_1LE1LA_1RF0RC_---1RE (bbch)	Jul 2025	mxdys	Probviously halting.
	BB(6)	1RB1LE_0LC0LB_1RD1LC_1RD1RA_1RF0LA_---1RE (bbch)	Jul 2024	Racheline	Probviously decidable. Estimated to have a 3/5 chance of becoming a translated cycler and a 2/5 chance of halting.
	BB(6)	1RB0RB_1LC1RE_1LF0LD_1RA1LD_1RC1RB_---1LC (bbch)	Aug 2024	mxdys, shown to be a Cryptid by DrDisentangle	Similar to Space Needle, probviously non-halting
	BB(6)	1RB1LA_0LC0RC_1LE1RD_1RE1RC_1LF0LA_---1LE (bbch)	April 2026	sheep, shown to be a Cryptid by Daniel Yuan	Similar to Space Needle, probviously non-halting
	BB(6)	1RB1LD_1RC0LE_1LA1RE_0LF1LA_1RB0RB_---0LB (bbch)	Feb 2025	Racheline	Probviously halting.
Fenrir	BBf(22)	[1/15, 27/77, 49/3, 10/49, 33/2] and 2 others	Mar 2026	Jason Yuen (@-d) and Claude Opus 4.6	Probviously non-halting.

The following machines have chaotic behavior, but have not been classified as Cryptids due to seemingly lacking a connection to any known open mathematical problems, such as Collatz-like problems.

• 1RB1RE_1LC0RA_0RD1LB_---1RC_1LF1RE_0LB0LE (bbch)
• 1RB0LD_1LC0RA_1RA1LB_1LA1LE_1RF0LC_---0RE (bbch)
• 1RB---0RB0LA2RA_2LB2LA3RA4LB0LB (bbch)
• 1RB3LA1LA1RA3RA_2LB2RA---4RB1LB (bbch)
• 1RB3LA1LA1RA1RA_2LB2RA---4RB1LB (bbch)
• 1RB3LB---4LA1RB_2LA4LA4LB3RB1RA (bbch) Analysis by @mxdys

Larger Cryptids

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

Name	BB domain	Machine	Date	Discoverer	Note
ZF	BB(432)	Wade's machine: https://codeberg.org/ajwade/turing_machine_explorer/src/commit/33b30300054242201a95679aacf7e74312bd8803b0df9a85d2314095efd6804e	2025	Wade, based on work by CatIsFluffy and O'Rear	The machine halts if and only if Zermelo–Fraenkel set theory is inconsistent.
PA	BB(372)	https://github.com/LegionMammal978/turing_machine_explorer/blob/main/pa.py	2026	LegionMammal	The machines halts if and only if Peano-Arithmetic is inconsistent. Discord announcement
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 Riemann Hypothesis is false.
	BB(120)	https://arxiv.org/abs/2609.30306	Sep 2026	Joseph M. Shunia	The machine halts if and only if Riemann Hypothesis is false.
	BB(104) and BB(95)	https://github.com/google-deepmind/cryptids/tree/main/artifacts/riemann_95	Oct 2026	Google DeepMind	The machine halts if and only if Riemann Hypothesis is false. Not independently verified.
Goldbach	BB(25)	https://gist.github.com/anonymous/a64213f391339236c2fe31f8749a0df6 Machine code: 1RB1RD_1LC1RB_0RA1LC_0LQ1RE_0LF1RG_0LC1LF_0LF0LH_1LQ1LI_0RJ0LI_1RK0LJ_0RL0RS_1RL0RM_1RN1RM_0LO0LU_0LP1LO_1RH1LX_1LR1LQ_0RK0LT_1LR1RS_---1RC_1LV1LU_0LW0LJ_0RK0LW_1RY1LX_1RE1RY (bbch)	2016	anonymous	The machine halts if and only if Goldbach's conjecture is false. Its behavior has been verified in Lean.
	BB(21)	https://github.com/google-deepmind/cryptids/tree/main/artifacts/goldbach_21 Machine code: 1LJ0RF_0RJ1RD_1RP1LC_---1RE_0LO1RG_1LQ1RF_0RH0LH_0LM1LU_1RB0LI_1RJ0RK_1RL1RK_0LM0LS_1LN1LM_1LO0LC_1LQ1LO_1RD1RP_0RA0LR_0RB1LR_1LT1LS_0LU0LI_0RB0LU (bbch)	Oct 2026	Google DeepMind	The machine halts if and only if Goldbach's conjecture is false. Not independently verified.
Erdős	BB(5,4) and BB(15)	https://docs.bbchallenge.org/other/powers_of_two_5_4.txt Machine code: 1RB3RA2RA1RB_0LC2RB1RA3RB_0LD1LC2LE3LC_3RE2RE---1RE_0RB1LE2LE3LE https://docs.bbchallenge.org/other/powers_of_two_15_2.txt Machine code: 1RB1RO_0RC0RC_0RD1RJ_0LE1RC_0LF1LK_0LG1LE_0LH1LF_1RI0LL_0RB1LK_1RC0RA_0LI1LN_1RM---_0RI0RO_0LK1LK_1LM1RA	Jul 2021	Tristan Stérin (@cosmo) 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." arxiv preprint
	BB(4,4)	1RB2RA1RB3RA_0LC3RB2RB1RA_1RZ1LD2LC3LC_0RA1LD2LD3LD (bbch)	Oct 2026	roromachine14	The machine halts if and only if the following conjecture is false: "For all n > 0, there is at least one 1 in the base-3 representation of 2^n - 1." Not independently verified. Announced on Discord
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	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.
	BB(14) and BB(10,3)	https://github.com/calr3/tinycryptids/tree/main/weakcollatz (includes Lean formalization) Machine code: 1LM0RB_1LC1RB_0LM0LD_1RE1LD_0RF0RB_0LN0LG_1LH1LG_0RK0RI_1RJ1RI_0LN1RF_0RL1RK_0RZ1LC_0RA1LM_1LM1LN (bbch) 2RG0RB---_1LC1RB2LC_0LI0LD2LD_1RE1LD1LF_2RC0RB---_0RJ2RG---_1RH1RG1RH_2LI1RC1RH_0RA1LI1LI_0LI1RJ1RZ (bbch)	Oct 2026	Charlie Reams	The machine halts if and only if the "weak Collatz conjecture" is false, as above. BB(14) verified by Shawn Ligocki.
Fermat's Last Theorem	BB(400)	Studies in Turing Machines (1965), pp. 81--82	1965	James Randels	From Randels' doctoral dissertation Studies in Turing Machines (1965). The machine was a cryptid until Wiles resolved Fermat's Last Theorem in 1994. The machine is not explicitly given, but there is a flowchart to construct the machine, and the state count is claimed to be less than 400.
	BB(127) and BB(90)	https://github.com/calr3/tinycryptids/tree/main/fermat (includes Lean formalization)	Oct 2026	Charlie Reams	The machine halts if and only if Fermat's Last Theorem is false, so it never halts. Not independently verified.
Bigfoot - compiled	BB(7)	0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB (bbch)	June 2024	@Iijil1	Compilation of Bigfoot into 2 symbols, there was a previous compilation with 8 states. Bigfoot Comment
Hydra - compiled	BB(9)	0RB0LD_1LC0LI_1LD1LB_0LE0RG_1RF0RH_1RA---_0RD0LB_0RA---_0RF1RZ (bbch) File:Hydra 9 states.txt	June 2024	@Iijil1	Compilation of Hydra into 2 symbols, all confirmed by Shawn Ligocki. @Iijil1 provided 24 TMs which all emulate the same behavior. Announced on Discord. Previous compilation had 10 states, by Daniel Yuan, also 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 1RB1LE_0LC0LB_0LD1LC_1RD1RA_---0LA with different values.