1RB1RZ 0RC0RE 1LD1LA 1LC0LG 0RF1LF 0RD1LF 1LB0LE - Revision history

Polygon: /* Analysis by Shawn Ligocki */ Added link to existing user page

2025-10-09T19:36:13Z

Analysis by Shawn Ligocki: Added link to existing user page

← Older revision		Revision as of 19:36, 9 October 2025
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	{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE\|halt}} is a tetrational halting [[BB(7)]] TM with sigma score over <math>10 \uparrow\uparrow 519</math>. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).		{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE\|halt}} is a tetrational halting [[BB(7)]] TM with sigma score over <math>10 \uparrow\uparrow 519</math>. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).

	== Analysis by Shawn Ligocki ==		== Analysis by [[User:Sligocki\|Shawn Ligocki]] ==
	This TM goes through 2 phases: Phase A and Phase B.		This TM goes through 2 phases: Phase A and Phase B.

Polygon: Added Category:BB(7)

2025-09-28T10:03:23Z

Added Category:BB(7)

← Older revision		Revision as of 10:03, 28 September 2025
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	It gets very lucky in Phase A: resetting 9 times before hitting a multiple of 3 and a little bit lucky in Phase B: resetting 4 times before hitting a remainder 2 factor.		It gets very lucky in Phase A: resetting 9 times before hitting a multiple of 3 and a little bit lucky in Phase B: resetting 4 times before hitting a remainder 2 factor.
			[[Category:BB(7)]]

Polygon: /* Analysis by Shawn Ligocki */ Fixed presumed typo

2025-08-18T10:42:52Z

Analysis by Shawn Ligocki: Fixed presumed typo

← Older revision		Revision as of 10:42, 18 August 2025
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	B(b, 288, 0) b = f1(f2^{72}(a)) = f1( f2^{125}(4) )		B(b, 288, 0) b = f1(f2^{72}(a)) = f1( f2^{125}(4) )
	B(c, 384, 0) c = f1(f2^{96}(b))		B(c, 384, 0) c = f1(f2^{96}(b))
	B(d, 512, 0) d = f1(f2^{128}(b))		B(d, 512, 0) d = f1(f2^{128}(c))
	Halt(2e + 692) e = f2^{170}(d)		Halt(2e + 692) e = f2^{170}(d)
	</pre>		</pre>

Polygon: Added "halt" to bbch-link

2025-08-16T18:34:35Z

Added "halt" to bbch-link

← Older revision		Revision as of 18:34, 16 August 2025
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	{{machine\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}		{{machine\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
	{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting [[BB(7)]] TM with sigma score over <math>10 \uparrow\uparrow 519</math>. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).		{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE\|halt}} is a tetrational halting [[BB(7)]] TM with sigma score over <math>10 \uparrow\uparrow 519</math>. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).

	== Analysis by Shawn Ligocki ==		== Analysis by Shawn Ligocki ==

Sligocki: Add note about luck and define shorthand notations.

2025-06-07T05:28:38Z

Add note about luck and define shorthand notations.

← Older revision		Revision as of 05:28, 7 June 2025
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	A(a, b) = 0^inf <F 10 1^a 00 1^b 0^inf		A(a, b) = 0^inf <F 10 1^a 00 1^b 0^inf
	B(a, b, c, d, e) = 0^inf <F 1^2a+1 00 1^2b 0^2c+1 1^d 00 1^e 0^inf		B(a, b, c, d, e) = 0^inf <F 1^2a+1 00 1^2b 0^2c+1 1^d 00 1^e 0^inf

			Shorthand:
			A(a) = A(a, 0)
			B(b, d, e) = B(0, b, 0, d, e)

	f1(x) = 2x+2		f1(x) = 2x+2
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	Phase A:		Phase A:
	Start --(13)--> A(1~~, 0~~)		Start --(13)--> A(1)
	A(3k~~, 0~~) -> B(0, 4~~, 0~~, 4k-3, 4)		A(3k) -> B(4, 4k-3, 4)
	A(3k+1~~, 0~~) -> A(4k+4~~, 0~~)		A(3k+1) -> A(4k+4)
	A(3k+2~~, 0~~) -> A(4k+6~~, 0~~)		A(3k+2) -> A(4k+6)

	Phase B:		Phase B:
	B(0, b~~, 0~~, 3k, e) -> B(0, f1(f2^k(b))~~, 0~~, 4k+e, 0)		B(b, 3k, e) -> B(f1(f2^k(b)), 4k+e, 0)
	B(0, b~~, 0~~, 3k+1, e) -> B(0, f2^{k+1}(b)~~, 0~~, 4k+e+4, 0)		B(b, 3k+1, e) -> B(f2^{k+1}(b), 4k+e+4, 0)
	B(0, b~~, 0~~, 3k+2, e) -> Halt(2 f2^k(b) + 4k + e + 12)		B(b, 3k+2, e) -> Halt(2 f2^k(b) + 4k + e + 12)
	</pre>		</pre>

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	If we ignore the <code>f1</code> calls and note that <math>f_2(x) > 2^x</math> then the sigma score at halt is larger than <math>e > f_2^{519}(4) > (2 \uparrow)^{519} 4 > 10 \uparrow\uparrow 519</math>.		If we ignore the <code>f1</code> calls and note that <math>f_2(x) > 2^x</math> then the sigma score at halt is larger than <math>e > f_2^{519}(4) > (2 \uparrow)^{519} 4 > 10 \uparrow\uparrow 519</math>.

			It gets very lucky in Phase A: resetting 9 times before hitting a multiple of 3 and a little bit lucky in Phase B: resetting 4 times before hitting a remainder 2 factor.

Sligocki: Fix math tag

2025-06-07T05:23:41Z

Fix math tag

← Older revision		Revision as of 05:23, 7 June 2025
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	{{machine\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}		{{machine\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
	{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting [[BB(7)]] TM with sigma score over $10 \uparrow\uparrow 519$. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).		{{TM\|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting [[BB(7)]] TM with sigma score over <math>10 \uparrow\uparrow 519</math>. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).

	== Analysis by Shawn Ligocki ==		== Analysis by Shawn Ligocki ==

Sligocki: Created page with "{{machine|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} {{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting BB(7) TM with sigma score over $10 \uparrow\uparrow 519$. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]). == Analysis by Shawn Ligocki == This TM goes through 2 phases: Phase A and Phase B.

 A(a, b) = 0^inf 
2025-06-07T05:23:12Z
Created page with "{{machine|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} {{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting BB(7) TM with sigma score over $10 \uparrow\uparrow 519$. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).  == Analysis by Shawn Ligocki == This TM goes through 2 phases: Phase A and Phase B.  <pre> A(a, b) = 0^inf <F 10 1^a 0..."
New page
{{machine|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}

{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}} is a tetrational halting [[BB(7)]] TM with sigma score over $10 \uparrow\uparrow 519$. It was found by Andrew Ducharme on 6 Jun 2025 ([https://discord.com/channels/960643023006490684/1369339127652159509/1380710649306288180 Discord link]).



== Analysis by Shawn Ligocki ==

This TM goes through 2 phases: Phase A and Phase B.



<pre>

A(a, b) = 0^inf <F 10 1^a 00 1^b 0^inf

B(a, b, c, d, e) = 0^inf <F 1^2a+1 00 1^2b 0^2c+1 1^d 00 1^e 0^inf



f1(x) = 2x+2

f2(x) = f1^x(4) = 6 2^b - 2



Phase A:

  Start --(13)--> A(1, 0)

  A(3k,   0) -> B(0, 4, 0, 4k-3, 4) 

  A(3k+1, 0) -> A(4k+4, 0)

  A(3k+2, 0) -> A(4k+6, 0)



Phase B:

  B(0, b, 0, 3k,   e) -> B(0, f1(f2^k(b)), 0, 4k+e,   0)

  B(0, b, 0, 3k+1, e) -> B(0, f2^{k+1}(b), 0, 4k+e+4, 0)

  B(0, b, 0, 3k+2, e) -> Halt(2 f2^k(b) + 4k + e + 12)

</pre>



The trajectory is:

<pre>

Phase A:

  1 4 8 14 22 32 46 64 88 120

Phase B:

  B(4, 157, 4)

  B(a, 216, 0)    a = f2^{53}(4)

  B(b, 288, 0)    b = f1(f2^{72}(a)) = f1( f2^{125}(4) )

  B(c, 384, 0)    c = f1(f2^{96}(b))

  B(d, 512, 0)    d = f1(f2^{128}(b))

  Halt(2e + 692)  e = f2^{170}(d)

</pre>



If we ignore the <code>f1</code> calls and note that <math>f_2(x) > 2^x</math> then the sigma score at halt is larger than <math>e > f_2^{519}(4) > (2 \uparrow)^{519} 4 > 10 \uparrow\uparrow 519</math>.