1RB2LC1RC 2LC---2RB 2LA0LB0RA - Revision history

Hipparcos: revise probvious halt step estimate

2026-11-07T20:32:20Z

revise probvious halt step estimate

← Older revision		Revision as of 20:32, 7 November 2026
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	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

	After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviously halts since jumping over this wall is very "unlikely". If this TM does in fact halt at that configuration, it is ~~estimated~~ to do so in ~~roughly 2 ×~~ 10<sup>~~410~~</sup> steps.<ref>https://discord.com/channels/960643023006490684/1259770474897080380/~~1568116988470108261~~</ref>		After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviously halts since jumping over this wall is very "unlikely". If this TM does in fact halt at that configuration, it is expected to do so in 10<sup>414</sup> to 10<sup>417</sup> steps.<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1568717661494448249</ref>

	The TM has been simulated for over 10<sup>27</sup> steps<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref>, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>		The TM has been simulated for over 10<sup>27</sup> steps<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref>, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>

Hipparcos: add probvious rough estimated halt time

2026-11-06T15:14:35Z

add probvious rough estimated halt time

← Older revision		Revision as of 15:14, 6 November 2026
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	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

	After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM ~~probviosly~~ halts since jumping over this wall is very "unlikely".		After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviously halts since jumping over this wall is very "unlikely". If this TM does in fact halt at that configuration, it is estimated to do so in roughly 2 × 10<sup>410</sup> steps.<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1568116988470108261</ref>

	The TM has been simulated for over 10<sup>27</sup> steps<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref>, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>		The TM has been simulated for over 10<sup>27</sup> steps<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref>, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>

Polygon: Moved reference away from the exponent

2026-11-03T11:42:51Z

Moved reference away from the exponent

← Older revision		Revision as of 11:42, 3 November 2026
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	After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".		After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".

	The TM has been simulated for over 10<sup>27</sup><ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref> ~~steps~~, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>		The TM has been simulated for over 10<sup>27</sup> steps<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref>, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>

	== dyuan01's Rules ==		== dyuan01's Rules ==

Sligocki: Undo revision 9537 by Δ⁵ (talk)

2026-10-28T14:50:05Z

Undo revision 9537 by Δ⁵ (talk)

← Older revision		Revision as of 14:50, 28 October 2026
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	{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}		{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}
	{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}}~~, also known as John Halter,~~ is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].		{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}} is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].

	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

Δ⁵ at 04:04, 25 October 2026

2026-10-25T04:04:56Z

← Older revision		Revision as of 04:04, 25 October 2026
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	{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}		{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}
	{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}} is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].		{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}}, also known as John Halter, is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].

	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

C1: Minor grammatical changes

2026-07-20T00:11:23Z

Minor grammatical changes

← Older revision		Revision as of 00:11, 20 July 2026
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	LegionMammal's rough timeline of this TM on 30 Apr 2025 ([https://discord.com/channels/960643023006490684/1259770474897080380/1367340727859679322 Discord link]):		LegionMammal's rough timeline of this TM on 30 Apr 2025 ([https://discord.com/channels/960643023006490684/1259770474897080380/1367340727859679322 Discord link]):

	# The machine (and its sibling) ~~pass~~ straight through various rounds of cleverly-written deciders		# The machine (and its sibling) passed straight through various rounds of cleverly-written deciders
	# dyuan ~~posts~~ his set of rules and ~~looks~~ into it a bit, Justin ~~notes~~ that he'd briefly looked at it some time back		# dyuan posted his set of rules and looked into it a bit, Justin noted that he'd briefly looked at it some time back
	# Shawn and savask ~~write~~ up some acceleration schemes, ~~find~~ empirical evidence that it repeatedly comes close to halting, and ~~speculate~~ that it ~~may~~ actually halt after some period of time		# Shawn and savask wrote up some acceleration schemes, found empirical evidence that it repeatedly comes close to halting, and speculated that it might actually halt after some period of time
	# I ~~take~~ a crack at it myself, this time in terms of chains starting from <code>A(1,c)</code> configs, ~~find~~ some <code>c</code> values leading to a halt (showing that there's no obvious structural barrier), and ~~conjecture~~ some heuristics for how long it should take to reach such a halting <code>c</code> value		# I took a crack at it myself, this time in terms of chains starting from <code>A(1,c)</code> configs, found some <code>c</code> values leading to a halt (showing that there's no obvious structural barrier), and conjectured some heuristics for how long it should take to reach such a halting <code>c</code> value
	# dyuan and I ~~nail~~ down the ideas of 'halter families' (collections of infinitely many halting <code>c</code> values so we don't have to brute-force them) and 'reachability analysis' (obtaining a strong probvious guess of whether a <code>c</code> value will or won't occur in the machine's actual forward behavior, assuming it hasn't halted beforehand)		# dyuan and I nailed down the ideas of 'halter families' (collections of infinitely many halting <code>c</code> values so we don't have to brute-force them) and 'reachability analysis' (obtaining a strong probvious guess of whether a <code>c</code> value will or won't occur in the machine's actual forward behavior, assuming it hasn't halted beforehand)
	# dyuan and I ~~race~~ to find a halting <code>c</code> value that 'explodes' (passes the reachability analysis), first within the 'trivial' halter family to no avail, then within all halter families (writing a program to enumerate halter families is extremely fiddly, at this point I treat some of my own code as a black box not to be touched)		# dyuan and I raced to find a halting <code>c</code> value that 'explodes' (passes the reachability analysis), first within the 'trivial' halter family to no avail, then within all halter families (writing a program to enumerate halter families is extremely fiddly, at this point I treat some of my own code as a black box not to be touched)
	# By dint of a somewhat more performant program, I ~~find~~ (and dyuan ~~confirms~~) the <math>c = \frac{3^{307}-8\,282\,708\,212}{13\,959\,275}</math> we all know and love, probviously sealing the machine's fate		# By dint of a somewhat more performant program, I found (and dyuan confirmed) the <math>c = \frac{3^{307}-8\,282\,708\,212}{13\,959\,275}</math> we all know and love, probviously sealing the machine's fate

	== savask's Rules ==		== savask's Rules ==

Polygon: Even further simulation found

2026-04-19T16:28:05Z

Even further simulation found

← Older revision		Revision as of 16:28, 19 April 2026
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	After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".		After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".

	The TM has been simulated for ~~1052884886930621967473049580 (~1e27)~~<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref> steps, reaching A(1,~~713176529181758~~(~~~7e14~~)).<ref>https://discord.com/channels/960643023006490684/~~960643023530762341~~/~~1275459473112170569~~</ref>		The TM has been simulated for over 10<sup>27</sup><ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref> steps, reaching A(1, 1059491543272883(~1e15)).<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1390819028137803829</ref>

	== dyuan01's Rules ==		== dyuan01's Rules ==

Polygon: Added simulation progress

2026-04-19T16:25:17Z

Added simulation progress

← Older revision		Revision as of 16:25, 19 April 2026
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	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

	After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".		After active exploration on the #bb3x3 channel by LegionMammal and dyuan, LegionMammal found (and dyuan confirmed) a configuration A(1,c) (defined [https://discord.com/channels/960643023006490684/1259770474897080380/1259968221218607145 here]) which halts and for which a huge "wall" of previous A(1, c') values all reach it. This gives strong evidence that the TM probviosly halts since jumping over this wall is very "unlikely".

			The TM has been simulated for 1052884886930621967473049580 (~1e27)<ref>https://discord.com/channels/960643023006490684/1259770474897080380/1324065684677988505</ref> steps, reaching A(1,713176529181758(~7e14)).<ref>https://discord.com/channels/960643023006490684/960643023530762341/1275459473112170569</ref>

	== dyuan01's Rules ==		== dyuan01's Rules ==
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	And as n gets way bigger, these ranges of repeat will increase exponentially.		And as n gets way bigger, these ranges of repeat will increase exponentially.

			== References ==

	[[Category:BB(3,3)]][[Category:Potential Cryptids]]		[[Category:BB(3,3)]][[Category:Potential Cryptids]]

Polygon: Moved from Category:Cryptids to Category:Potential Cryptids

2026-03-30T14:18:10Z

Moved from Category:Cryptids to Category:Potential Cryptids

← Older revision		Revision as of 14:18, 30 March 2026
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	And as n gets way bigger, these ranges of repeat will increase exponentially.		And as n gets way bigger, these ranges of repeat will increase exponentially.
	[[Category:BB(3,3)]][[Category:Cryptids]]		[[Category:BB(3,3)]][[Category:Potential Cryptids]]

Sligocki: Remove note on "current" work and move several rulesets that aren't used any more to bottom of page.

2025-11-02T21:10:45Z

Remove note on "current" work and move several rulesets that aren't used any more to bottom of page.

Show changes

← Older revision		Revision as of 14:50, 28 October 2026
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	{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}		{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}
	{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}}~~, also known as John Halter,~~ is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].		{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}} is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].

	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.

← Older revision		Revision as of 04:04, 25 October 2026
Line 1:		Line 1:
	{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}		{{machine\|1RB2LC1RC_2LC---2RB_2LA0LB0RA}} {{unsolved\|Does this TM halt? If so, how many steps does it take to halt?}}
	{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}} is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].		{{TM\|1RB2LC1RC_2LC---2RB_2LA0LB0RA\|undecided}}, also known as John Halter, is a [[BB(3,3)]] [[holdout]] which appears to [[probviously]] halt. If it can be proven to halt, it will be the BB(3,3) champion in terms of both steps and tape symbols. However, it could also turn out to be a probviously halting [[Cryptid]].

	This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.		This is holdout #758 on Justin's 3x3 mugshots. After about 1.8 million steps and up to some relabelling, it is equivalent to holdout #153: {{TM\|1RB0LB0RC_2LC2LA1RA_1RA1LC---}}. And if you start in state C it is a [[permutation]] of the same machine. Together, they simulate a complex set of [[Collatz-like]] rules with two decreasing parameters.