BB(4,3): Difference between revisions

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TODO
TODO


The current champion appears to be {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}} which was discovered by Pavel Kropitz in May 2024 and analyzed by Racheline in Feb 2025 which demonstrates the lower bounds:
The current [[Champions#3-Symbol TMs|champion]] appears to be {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}} which was discovered by Pavel Kropitz in May 2024 and analyzed by Racheline in Feb 2025 which demonstrates the lower bounds:


<math display="block">S(4,3) > \Sigma(4,3) > 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math>
<math display="block">S(4,3) > \Sigma(4,3) > 2 \uparrow\uparrow\uparrow 2^{2^{32}}</math>
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https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120
https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120


* {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}: 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
* {{TM|0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}: 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
* {{TM|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD}}: 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
* {{TM|0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD|halt}}: 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
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD}}: 1 Z> 1^((8*<7; (6*2^((4b + 14)) - 4); (6*2^((48*2^(21) - 2)) - 4)> + 33)) 2  
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD|halt}}: 1 Z> 1^((8*<7; (6*2^((4b + 14)) - 4); (6*2^((48*2^(21) - 2)) - 4)> + 33)) 2  
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA}}: 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
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA}}: 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
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD}}: 1 Z> 1^((2*<(<(<(16*2^(92) - 3); (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<(24*2^((24*2^(<(24*2^((24*2^(92) - 3)) - 2); (24*2^(b) - 4); 92>) - 3)) - 1); (24*2^(b) - 4); 2>) - 3)) - 11)> + 8)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 5)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 19))
* {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}}: 1 Z> 1^((2*<(<(<(16*2^(92) - 3); (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<(24*2^((24*2^(<(24*2^((24*2^(92) - 3)) - 2); (24*2^(b) - 4); 92>) - 3)) - 1); (24*2^(b) - 4); 2>) - 3)) - 11)> + 8)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 5)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 19))
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB}}: 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
* {{TM|1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB|halt}}: 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
* {{TM|1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD}}: 1 Z> 1^(162*3^((3*<(243*3^(6) - 5)/2; (<(54*3^((3b + 11)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1); (<(54*3^((3*<(54*3^(7) - 3); (54*3^((3b + 14)/2) - 6); (54*3^((81*3^(7) - 2)) - 6)> + 14)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1)> + 11)/2)) 2
* {{TM|1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD|halt}}: 1 Z> 1^(162*3^((3*<(243*3^(6) - 5)/2; (<(54*3^((3b + 11)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1); (<(54*3^((3*<(54*3^(7) - 3); (54*3^((3b + 14)/2) - 6); (54*3^((81*3^(7) - 2)) - 6)> + 14)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1)> + 11)/2)) 2


[[Category:BB Domains]]
[[Category:BB Domains]]

Latest revision as of 18:56, 16 August 2025

TODO

The current champion appears to be 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch) which was discovered by Pavel Kropitz in May 2024 and analyzed by Racheline in Feb 2025 which demonstrates the lower bounds:

I say appears to be because this list of "Potential Champions" below has not yet been fully investigated.

Potential Champions

In May 2024, Pavel Kropitz found 7 halting TMs that run for a large number of steps, but have not been analyzed in detail:

https://discord.com/channels/960643023006490684/1026577255754903572/1243253180297646120

  • 0RB1RZ0RB_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch): 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
  • 0RB1RZ1RC_1RC1LB2LB_1LB2RD1LC_1RA2RC0LD (bbch): 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
  • 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_2RB2RA2RD (bbch): 1 Z> 1^((8*<7; (6*2^((4b + 14)) - 4); (6*2^((48*2^(21) - 2)) - 4)> + 33)) 2
  • 1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ0RA (bbch): 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
  • 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch): 1 Z> 1^((2*<(<(<(16*2^(92) - 3); (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<(24*2^((24*2^(<(24*2^((24*2^(92) - 3)) - 2); (24*2^(b) - 4); 92>) - 3)) - 1); (24*2^(b) - 4); 2>) - 3)) - 11)> + 8)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 5)/3; (24*2^((24*2^(<(b + 10); (24*2^(b) - 4); 2>) - 3)) - 11); (24*2^((24*2^(<1; (24*2^(b) - 4); 2>) - 3)) - 11)> + 19))
  • 1RB1LA2LA_1LA2RC1LB_1RD2RB0LC_0RA1RZ1RB (bbch): 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
  • 1RB2LB0LB_2LC2LA0LA_2RD1LC1RZ_1RA2LD1RD (bbch): 1 Z> 1^(162*3^((3*<(243*3^(6) - 5)/2; (<(54*3^((3b + 11)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1); (<(54*3^((3*<(54*3^(7) - 3); (54*3^((3b + 14)/2) - 6); (54*3^((81*3^(7) - 2)) - 6)> + 14)/2) - 2); (54*3^((3b + 14)/2) - 6); (54*3^(7) - 6)> + 1)> + 11)/2)) 2
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