0RB1RZ0RB 1RC1LB2LB 1LB2RD1LC 1RA2RC0LD - Revision history

Polygon: as --> in

2025-10-23T17:31:54Z

as --> in

← Older revision		Revision as of 17:31, 23 October 2025
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	<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}) \text{ and } 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}+1)</math>		<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}) \text{ and } 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}+1)</math>

	steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 7 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>		steps. The TM was discovered by Pavel Kropitz in May 2024 in a group of 7 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>

	Pavel listed the halting tape as:		Pavel listed the halting tape as:

RobinCodes: Corrected the number of TMs found by Pavel

2025-10-23T15:12:59Z

Corrected the number of TMs found by Pavel

← Older revision		Revision as of 15:12, 23 October 2025
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	<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}) \text{ and } 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}+1)</math>		<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}) \text{ and } 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}+1)</math>

	steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>		steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 7 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>

	Pavel listed the halting tape as:		Pavel listed the halting tape as:

Polygon: Added Category:BB(4,3)

2025-10-04T11:00:52Z

Added Category:BB(4,3)

← Older revision		Revision as of 11:00, 4 October 2025
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	== References ==		== References ==
	<references />		<references />
			[[Category:BB(4,3)]]

Polygon: Added upper bound

2025-08-18T13:58:20Z

Added upper bound

← Older revision		Revision as of 13:58, 18 August 2025
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	{{machine\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}		{{machine\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}
	{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for ~~around~~		{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for between

	<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1})</math>		<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}) \text{ and } 2 \uparrow\uparrow\uparrow (2^{2^{32}+1}+1)</math>

	steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>		steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>

Polygon: It's actually slightly larger

2025-08-18T10:30:10Z

It's actually slightly larger

← Older revision		Revision as of 10:30, 18 August 2025
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	{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for around		{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for around

	<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math>		<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1})</math>

	steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>		steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>

Polygon: Removed excess line

2025-08-11T09:53:55Z

Removed excess line

← Older revision		Revision as of 09:53, 11 August 2025
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	{{machine\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}		{{machine\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}

	{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for around		{{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is a halting [[BB(4,3)]] machine that appears to run for around

Racheline at 14:36, 8 February 2025

2025-02-08T14:36:36Z

← Older revision		Revision as of 14:36, 8 February 2025
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	== Equivalent TMs ==		== Equivalent TMs ==

	The TMs {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} are equivalent to {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, with the exact same halting configuration <code>0^inf 1 2^(σ-10) 101211 Z> 1221 0^inf</code>, where <code>σ = 5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> is the total number of nonzero symbols.		The TMs {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} [https://discord.com/channels/960643023006490684/1331570843829932063/1337236324846927932 are equivalent] to {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, with the exact same halting configuration <code>0^inf 1 2^(σ-10) 101211 Z> 1221 0^inf</code>, where <code>σ = 5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> is the total number of nonzero symbols.

	To see that {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is equivalent, simply notice that the situation <code>A> 20</code> never occurs in any of the rules in the above analysis, or inside the low-level bell cycles, and that <code>A> 21</code> and <code>A> 22</code> behave the same in both TMs, except that they take two more steps in {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}. Since the A2 transition is the only difference between the two, this means the TMs only differ in the number of steps it takes to halt (and even that difference is insignificant, on the order of σ = <code>5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> while the total number of steps is around σ<sup>2</sup>. {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}} and {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} are just {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} and {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} respectively, but started one step later, so that their halting time is 1 step smaller.		To see that {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is equivalent, simply notice that the situation <code>A> 20</code> never occurs in any of the rules in the above analysis, or inside the low-level bell cycles, and that <code>A> 21</code> and <code>A> 22</code> behave the same in both TMs, except that they take two more steps in {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}. Since the A2 transition is the only difference between the two, this means the TMs only differ in the number of steps it takes to halt (and even that difference is insignificant, on the order of σ = <code>5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> while the total number of steps is around σ<sup>2</sup>). {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}} and {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} are just {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} and {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} respectively, but started one step later, so that their halting time is 1 step smaller.

	== References ==		== References ==
	<references />		<references />

Racheline at 14:26, 8 February 2025

2025-02-08T14:26:57Z

← Older revision		Revision as of 14:26, 8 February 2025
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	this continues the same way as if the 0^8 was a 0^10 until the last few steps, so the tape differs from 0^inf 1 <D 0^2 2^(5*2^(2^(f^g^n1(n0)(0)+1)+2)-4) 11221 in a small amount of symbols on the left end and the right end, which you can easily count by running a smaller example		this continues the same way as if the 0^8 was a 0^10 until the last few steps, so the tape differs from 0^inf 1 <D 0^2 2^(5*2^(2^(f^g^n1(n0)(0)+1)+2)-4) 11221 in a small amount of symbols on the left end and the right end, which you can easily count by running a smaller example
	</pre>		</pre>

			== Equivalent TMs ==

			The TMs {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}}, {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} are equivalent to {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}, with the exact same halting configuration <code>0^inf 1 2^(σ-10) 101211 Z> 1221 0^inf</code>, where <code>σ = 5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> is the total number of nonzero symbols.

			To see that {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} is equivalent, simply notice that the situation <code>A> 20</code> never occurs in any of the rules in the above analysis, or inside the low-level bell cycles, and that <code>A> 21</code> and <code>A> 22</code> behave the same in both TMs, except that they take two more steps in {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}}. Since the A2 transition is the only difference between the two, this means the TMs only differ in the number of steps it takes to halt (and even that difference is insignificant, on the order of σ = <code>5*2^(2^(f^g^n1(n0)(0)+1)+2)+7</code> while the total number of steps is around σ<sup>2</sup>. {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA\|halt}} and {{TM\|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB\|halt}} are just {{TM\|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} and {{TM\|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD\|halt}} respectively, but started one step later, so that their halting time is 1 step smaller.

	== References ==		== References ==
	<references />		<references />

Sligocki: Created page with "{{machine|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}} {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} is a halting BB(4,3) machine that appears to run for around $2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)$ steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120 Racheline analyzed the ma..."

2025-02-07T19:47:58Z

Created page with "{{machine|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}} {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} is a halting BB(4,3) machine that appears to run for around <math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math> steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the ma..."

New page

{{machine|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}

{{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} is a halting [[BB(4,3)]] machine that appears to run for around

<math display="block">2 \uparrow\uparrow\uparrow (2^{2^{32}+1}-1)</math>

steps. The TM was discovered by Pavel Kropitz in May 2024 as a group of 6 long-running halting BB(4,3) TMs.<ref>https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120</ref> Racheline analyzed the machine by hand in Feb 2025, validating the result and provided the step estimate listed above.<ref>https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718</ref>

Pavel listed the halting tape as:

<pre>
1 2^((80*2^((<(8*2^((8*2^(29) - 2)) - 5); (<(80*2^((b - 10)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4); (<(80*2^((<(80*2^((8*2^((8*2^(29) - 2)) - 3)) - 13)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> - 6)/5) - 17)/9; (40*2^((8*2^((a - 11)/5) - 2)) - 4); (40*2^(2) - 4)> + 4)> - 10)/5) - 3)) 1 0 1 2 1^2 Z> 1 2^2 1
</pre>

== Analysis by racheline ==
https://discord.com/channels/960643023006490684/1331570843829932063/1337228898068463718

<pre>
f(n) = 2^2^(n+1)
g(n) = (5*2^(2^(f^n(0)+1)+2)-8)/9
n0 = (5*2^(2^(2^32+1)+1)-4)/9
n1 = 2^(2^32+1)-4
0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD halts with 5*2^(2^(f^g^n1(n0)(0)+1)+2)+7 nonzero symbols on the tape, after roughly (that)^2 steps
that's around 2^^^(2^(2^32+1)-1)
the rules necessary for verification:
0^inf 1 <D 0^(5n) 2^4 ->
0^inf 1 <D 0^(5*2^n+2)

0^inf 1 <D 0^(5n+2) 2^5 ->
0^inf 1 <D 0^(5*2^(n+1))

0^inf 1 <D 0^(5n) 221122 ->
0^inf 1 <D 0^(5*2^n+4)

0^inf 1 <D 0^(5n+4) 1 0^5 ->
0^inf 1 <D 0^2 2^23 1 0^(5*2^(n+2)-22) 1011221

0^inf 1 <D 0^(5n) 1 0^10 ->
0^inf 1 <D 0^2 2^(5*2^(n+1)) 11221

0^inf 1 <D 0^(5n+2) 2222112 ->
0^inf 1 <D 0^(5*2^(n+1)+2)

0^inf 1 <D 0^(5n+2) 21 0^10 ->
0^inf 1 <D 0^2 2^(5*2^(n+2)-4) 11221

0^inf 1 <D 0^(5n+2) 2^9 ->
0^inf 1 <D 0^(5*2^(n+1)) 2^4 ->
0^inf 1 <D 0^(5*2^2^(n+1)+2) =
0^inf 1 <D 0^(5f(n)+2)

0^inf 1 <D 0^2 2^(9n) ->
0^inf 1 <D 0^(5f^n(0)+2)

0^inf 1 <D 0^2 2^(9n+4) 11221 0^10 ->
0^inf 1 <D 0^(5f^n(0)+2) 222211221 0^10 ->
0^inf 1 <D 0^(5*2^(f^n(0)+1)+2) 21 ->
0^inf 1 <D 0^2 2^(5*2^(2^(f^n(0)+1)+2)-4) 11221 =
0^inf 1 <D 0^2 2^(9g(n)+4) 11221

0^inf 1 <D 0^2 2^(9n+4) 11221 0^(10m) ->
0^inf 1 <D 0^2 2^(9g^m(n)+4) 11221

0^inf 1 <D 0^2 2^16 11221 0^inf
0^inf 1 <D 0^10 2^11 11221 0^inf
0^inf 1 <D 0^22 2^7 11221 0^inf
0^inf 1 <D 0^160 2211221 0^inf
0^inf 1 <D 0^(5*2^32+4) 1 0^inf
0^inf 1 <D 0^2 2^23 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^10 2^18 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^22 2^14 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^160 2^9 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^(5*2^32+2) 2^5 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^(5*2^(2^32+1)) 1 0^(5*2^(2^32+2)-22) 1011221 0^inf
0^inf 1 <D 0^2 2^(5*2^(2^(2^32+1)+1)) 11221 0^(5*2^(2^32+2)-32) 1011221 0^inf =
0^inf 1 <D 0^2 2^(9n0+4) 11221 0^(10n1+8) 1011221 0^inf
0^inf 1 <D 0^2 2^(9g^n1(n0)+4) 11221 0^8 1011221 0^inf
0^inf 1 <D 0^(5*2^(f^g^n1(n0)(0)+1)+2) 21 0^8 1011221 0^inf
this continues the same way as if the 0^8 was a 0^10 until the last few steps, so the tape differs from 0^inf 1 <D 0^2 2^(5*2^(2^(f^g^n1(n0)(0)+1)+2)-4) 11221 in a small amount of symbols on the left end and the right end, which you can easily count by running a smaller example
</pre>

== References ==
<references />