BB(7): Difference between revisions

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The 7-state, 2-symbol Busy Beaver problem, '''BB(7)''', refers to the unsolved 7<sup>th</sup> value of the [[Busy Beaver function]]. With the compilation of the [[Cryptid]] machine [[Bigfoot]] into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a [[Collatz-like]] problem in order to solve BB(7).
The 7-state, 2-symbol Busy Beaver problem, '''BB(7)''', refers to the unsolved 7<sup>th</sup> value of the [[Busy Beaver function]]. With the compilation of the [[Cryptid]] machine [[Bigfoot]] into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a [[Collatz-like]] problem in order to solve BB(7).


The current BB(7) champion {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}} was discovered by Pavel Kropitz in May 2025, proving the lower bound: <math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>
The current BB(7) [[champion]] {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}} was discovered by Pavel Kropitz in May 2025, proving the lower bound: <math display="block">S(7) > \Sigma(7) > 2 \uparrow^{11} 2 \uparrow^{11} 3</math>


== History ==
== History ==
Line 8: Line 8:
In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.
In May 2025, mxdys shared [https://github.com/ccz181078/TM C++ code] that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.


Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB}}, with sigma score ~10 ↑↑ 46. A few days later, Pavel found a TM that outpaces all of them.
Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, {{TM|1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB|halt}} and {{TM|1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC|halt}}, with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found {{TM|1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB|halt}}, with sigma score ~10 ↑↑ 46. A few days later, Pavel found a TM that outpaces all of them.


Pavel's champion is enumerated in subtask 243308.
Pavel's champion is enumerated in subtask 243308.
== Cryptids ==
BB(7) has not been seriously investigated by hand, so no native BB(7) [[Cryptids]] have yet been discovered.
[[Probviously]] non-halting Cryptids:
{{TM|0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB}}, [[Bigfoot]] (a [[BB(3,3)]] Cryptid) compiled into a 2-symbol TM by Iijil in 2024.


== Top Halters ==
== Top Halters ==
Based on limited search through a subset of the 1 million subtasks from mxdys's code, the top 20 scoring known machines are:
The top 20 scoring known machines are:
{| class="wikitable sortable"
{| class="wikitable sortable"
!TM
!TM
Line 19: Line 26:
!Discoverer
!Discoverer
|-
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|@gerbil5709, Terry Ligocki
|@gerbil5709, Terry Ligocki
|-
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
|10 ↑↑ 286.17
|10 ↑↑ 286.17
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
|10 ↑↑ 246.32
|10 ↑↑ 246.32
|@Iijil
|@Iijil
|-
|-
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG}}
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA|halt}}
|10 ↑↑ 246.32
|@star, Terry Ligocki
|-
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
|10 ↑↑ 243.88
|10 ↑↑ 243.88
|@Iijil, Andrew Ducharme
|@Iijil, Andrew Ducharme
|-
|-
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
|10 ↑↑ 228.78
|10 ↑↑ 228.78
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG}}
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG}}
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD}}
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA}}
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|@C7X
|@C7X
|-
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|@Iijil, Terry Ligocki
|@Iijil, Terry Ligocki
|-
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ|halt}}
|10 ↑↑ 192.67
|@Iijil, Terry Ligocki
|-
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LG_1RF0RA_0RA0LA_1RB1RZ}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|@Iijil, Terry Ligocki
|@Iijil, Terry Ligocki
Line 107: Line 114:
!Discoverer
!Discoverer
|-
|-
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3</math>
|Pavel Kropitz
|Pavel Kropitz
|-
|-
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
|10 ↑↑ 286.17
|10 ↑↑ 286.17
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
|10 ↑↑ 246.32
|10 ↑↑ 246.32
|@Iijil
|@Iijil
|-
|-
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG}}
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
|10 ↑↑ 243.88
|10 ↑↑ 243.88
|@Iijil, Andrew Ducharme
|@Iijil, Andrew Ducharme
|-
|-
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
|10 ↑↑ 228.78
|10 ↑↑ 228.78
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG}}
|{{TM|1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA}}
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA|halt}}
|10 ↑↑ 188.28
|10 ↑↑ 188.28
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC|halt}}
|10 ↑↑ 140.28
|10 ↑↑ 140.28
|@stokastic
|@stokastic
|-
|-
|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA}}
|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA|halt}}
|10 ↑↑ 136.64
|10 ↑↑ 136.64
|Katelyn Doucette, Andrew Ducharme
|Katelyn Doucette, Andrew Ducharme
|-
|-
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG|halt}}
|10 ↑↑ 133.85
|10 ↑↑ 133.85
|@poppuncher
|@poppuncher
|-
|-
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF}}
|{{TM|1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF|halt}}
|10 ↑↑ 129.24
|10 ↑↑ 129.24
|@Iijil
|@Iijil
|-
|-
|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD}}
|{{TM|1RB0RG_1LC0RE_1LF1LD_0LE1LC_1RA1RB_1LD0LF_1RZ0RF|halt}}
|10 ↑↑ 127.52
|Andrew Ducharme
|-
|{{TM|1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD|halt}}
|10 ↑↑ 126.20
|10 ↑↑ 126.20
|@stokastic
|@stokastic
|-
|-
|{{TM|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ}}
|{{TM|1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ|halt}}
|10 ↑↑ 124.86
|10 ↑↑ 124.86
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ}}
|{{TM|1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ|halt}}
|10 ↑↑ 116.98
|10 ↑↑ 116.98
|Terry Ligocki
|Terry Ligocki
|-
|-
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG}}
|{{TM|1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG|halt}}
|10 ↑↑ 116.05
|10 ↑↑ 116.05
|
|
|-
|-
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ|halt}}
|10 ↑↑ 115.52
|10 ↑↑ 115.52
|@prurq
|@prurq
|-
|-
|{{TM|1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ}}
|{{TM|1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ|halt}}
|10 ↑↑ 114.83
|10 ↑↑ 114.83
|Andrew Ducharme
|Andrew Ducharme
|-
|-
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ|halt}}
|10 ↑↑ 114.60
|10 ↑↑ 114.60
|Shawn Ligocki
|Shawn Ligocki
|-
|{{TM|1RB0RE_0RC1LC_0LD1LF_1LE0LG_1RA0RC_0LB1LA_1LB1RZ}}
|10 ↑↑ 114.57
|Andrew Ducharme
|}
|}


== Current Progress ==
== Phase 1 ==
This is a summary of the 1 million subtasks from mxdys's code that have been executed and their output processed by Shawn Ligocki's linear rule code.
Phase 1's first two stages were carried out from May 2025 to July 2025. The table below summaries some of that activity and was used to coordinate the effort of doing the raw computation. Fourteen people (see below) contributed directly and the overall bbchallenge group participated in [https://discord.com/channels/960643023006490684/1369339127652159509 discord discussions], etc.
{| class="wikitable sortable defaultleft"
 
Stage 1, "enumeration" in the table, involved running 1 million subtasks using mxdys's code in 100 batches of 10 thousand subtasks.
 
Stage 2, "linear rule" in the table, processing the output of Stage 1 using Shawn Ligocki's linear rule code which also used a few other deciders, e.g., a version of CTL.
 
Stage 3, the final stage of Phase 1, is the compilation, verification, and presentation of the final results from Phase 1. It is ongoing but should be completed during August 2025.
 
{| class="wikitable sortable"
! rowspan="2" |Task range
! rowspan="2" |Task range
! rowspan="2" |Done by
! rowspan="2" |Done by
Line 207: Line 221:
|Yes
|Yes
|1,545,673
|1,545,673
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD}}
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD|halt}}
|10 ↑↑ 246.32
|10 ↑↑ 246.32
|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
|[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD Google Drive folder]
Line 218: Line 232:
|Yes
|Yes
|2,279,734
|2,279,734
|{{TM|1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG}}
|{{TM|1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG|halt}}
|10 ↑↑ 93.81
|10 ↑↑ 93.81
|
|
[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD @Iijil]<br/>
[https://drive.google.com/drive/folders/1wniwrAuvsHfkvro8Tg65WAMNZEuIekzD @Iijil]<br/>
[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|05-09xxxx
|05-09xxxx
Line 231: Line 245:
|Yes
|Yes
|3,889,955
|3,889,955
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG}}
|{{TM|1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG|halt}}
|10 ↑↑ 243.88
|10 ↑↑ 243.88
|
|
Line 242: Line 256:
|Yes
|Yes
|2,708,888
|2,708,888
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
Line 251: Line 265:
|Yes
|Yes
|1,192,442
|1,192,442
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ}}
|{{TM|1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ|halt}}
|10 ↑↑ 114.60
|10 ↑↑ 114.60
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|-
|-
|14-16xxxx
|14-16xxxx
Line 260: Line 274:
|Yes
|Yes
|2,701,637
|2,701,637
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA}}
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA|halt}}
|10 ↑↑ 188.28
|10 ↑↑ 188.28
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
Line 271: Line 285:
|Yes
|Yes
|1,898,156
|1,898,156
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ}}
|{{TM|1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|
|
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|19xxxx
|19xxxx
Line 283: Line 297:
|Yes
|Yes
|Yes
|Yes
|1,601,356
|1,099,752
|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA}}
|{{TM|1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA|halt}}
|10 ↑↑ 136.64
|10 ↑↑ 136.64
|[https://drive.google.com/drive/folders/1-eGxVc3kmGIEJFShG4olPX3sGci2SPaA?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/1-eGxVc3kmGIEJFShG4olPX3sGci2SPaA?usp=sharing Google Drive folder]
Line 293: Line 307:
|Yes
|Yes
|4,528,827
|4,528,827
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA}}
|{{TM|1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
| [https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
| [https://drive.google.com/drive/folders/11iGTKsvu2Y7aFrwOcWS1LYvcN6i_7-JM?usp=sharing Google Drive folder]
Line 302: Line 316:
|Yes
|Yes
|712,356
|712,356
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}*
|{{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}*
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3^*</math>
|data-sort-value="10 ↑↑ 9999"|<math>2 \uparrow^{11} 2 \uparrow^{11} 3^*</math>
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
Line 311: Line 325:
|Yes
|Yes
|10,339,816
|10,339,816
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC}}
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC|halt}}
|10 ↑↑ 140.28
|10 ↑↑ 140.28
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]  
|[https://drive.google.com/drive/folders/16_qIdWWD-wolj6zURB5ZSbY-otI4zoUF?usp=sharing Google Drive folder]  
Line 320: Line 334:
|Yes
|Yes
|4,894,047
|4,894,047
|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE}}
|{{TM|1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|-
|-
|40-47xxxx
|40-47xxxx
Line 329: Line 343:
|Yes
|Yes
|6,181,327
|6,181,327
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE}}
|{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/16uDjgOahkhAMWv3v-YWmxJG7xxsBvj4h?usp=sharing Google Drive folder]
|-
|-
|48xxxx
|48xxxx
|@star
|
@star<br/>
Terry Ligocki
|Yes
|Yes
|Yes
|No
|727,875
|954,005
|{{TM|1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA|halt}}
|TBD
|10 ↑↑ 246.32
|TBD
|
|[https://drive.google.com/file/d/1HbIX46_6V-etFWTv4FvWZmb7AHIiWB1v/view?usp=sharing Google Drive file]
[https://drive.google.com/file/d/1HbIX46_6V-etFWTv4FvWZmb7AHIiWB1v/view?usp=sharing @star]<br/>
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|49xxxx
|49xxxx
Line 349: Line 367:
|Yes
|Yes
|804,722
|804,722
|{{TM|1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG}}
|{{TM|1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG|halt}}
|10 ↑↑ 126.20
|10 ↑↑ 126.20
|
|
[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Tobiáš Brichta]<br/>
[https://drive.google.com/drive/folders/1-csgJ5uSIX3SKlqTkSnhkUuEYLKgCw81 Tobiáš Brichta]<br/>
[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|50xxxx
|50xxxx
Line 362: Line 380:
|Yes
|Yes
|797,224
|797,224
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ}}
|{{TM|1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ|halt}}
|10 ↑↑ 115.52
|10 ↑↑ 115.52
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
|[https://drive.google.com/drive/folders/145H4sT4F9KJYGSrlIETZdBOIMR7krLQm Google Drive folder]
Line 373: Line 391:
|Yes
|Yes
|3,016,175
|3,016,175
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC}}
|{{TM|1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC|halt}}
|10 ↑↑ 140.28
|10 ↑↑ 140.28
|
|
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|54-59xxxx
|54-59xxxx
Line 384: Line 402:
|Yes
|Yes
|5,689,850
|5,689,850
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA}}
|{{TM|1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA|halt}}
|10 ↑↑ 188.28
|10 ↑↑ 188.28
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|-
|-
|60-64xxxx
|60-64xxxx
Line 395: Line 413:
|Yes
|Yes
|3,817,876
|3,817,876
||{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE}}
||{{TM|1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE|halt}}
|10 ↑↑ 519.20
|10 ↑↑ 519.20
|
|
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1kAvBebeF09CEVocCk5bGKlDJfRN8co_i?usp=sharing @gerbil5709]<br/>
[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Terry Ligocki]
[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Terry Ligocki]
|-
|-
|65-68xxxx
|65-68xxxx
Line 406: Line 424:
|Yes
|Yes
|3,076,778
|3,076,778
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD}}
|{{TM|1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD|halt}}
|10 ↑↑ 192.67
|10 ↑↑ 192.67
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|-
|-
|69xxxx
|69xxxx
Line 415: Line 433:
|Yes
|Yes
|1,053,119
|1,053,119
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG}}
|{{TM|1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG|halt}}
|10 ↑↑ 133.85
|10 ↑↑ 133.85
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1KlCZqXxqVPuBPkDcCBocuMPA8paq9b8P?usp=drive_link Google Drive folder]
Line 424: Line 442:
|Yes
|Yes
|1,899,094
|1,899,094
|{{TM|1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD}}
|{{TM|1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD|halt}}
|10 ↑↑ 77.50
|10 ↑↑ 77.50
|[https://github.com/jhuang97/bb7x2/releases Github release]
|[https://github.com/jhuang97/bb7x2/releases Github release]
Line 433: Line 451:
|Yes
|Yes
|7,627,514
|7,627,514
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ}}
|{{TM|1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ|halt}}
|10 ↑↑ 228.78
|10 ↑↑ 228.78
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|-
|-
|80-81xxxx
|80-81xxxx
Line 442: Line 460:
|Yes
|Yes
|1,537,533
|1,537,533
|{{TM|1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC}}
|{{TM|1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC|halt}}
|10 ↑↑ 74.85
|10 ↑↑ 74.85
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
|[https://drive.google.com/drive/folders/1TpuEC7KottEmvsFnCREugnlVMPaY5ZHi?usp=sharing Google Drive folder]
Line 451: Line 469:
|Yes
|Yes
|15,673,786
|15,673,786
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ}}
|{{TM|1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ|halt}}
|10 ↑↑ 286.17
|10 ↑↑ 286.17
|[https://drive.google.com/drive/folders/1yQFLcznvNzEF9uWXL1xkJhhfxPDtbC7x?usp=drive_link Google Drive folder]
|[https://drive.google.com/drive/folders/1lyYN2wznnrfM0dg-dKprHODeYaTxdtzP?usp=drive_link Google Drive folder]
|}
|}
<nowiki>*</nowiki>The current BB(7) champion TM {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF}}* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.
<nowiki>*</nowiki>The current BB(7) champion TM {{TM|1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF|halt}}* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.
[[Category:BB Domain]]
 
== Exploration after Phase 1 ==
People are now looking at reducing the number of holdouts (~85M TMs) after Phase 1. They are trying different deciders not used in Phase 1 and different parameters with the deciders used in Phase 1. This table is somewhere they can put the results of these explorations so that there is a record of what is being done. It is hoped that this will inspire everyone to contribute when they can, a reference point for [https://discord.com/channels/960643023006490684/1369339127652159509 discord discussions], and something that can be questioned and/or verified.
 
{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |% Reduced
!rowspan="2" |Runtime (hours)
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Source
|-
!Input
!Output
!Decided
!Processed
|-
|style="text-align:center" |Shawn Ligocki
|858,538
|733,830
|14.5%
|5.0
|6.9282
|47.6966
|style="text-align:left" |[[Translated Cycler]] and [[CPS]] on <code>7x2_p01_s02_holdouts_rand_13.txt</code>
|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1403423336293208164 Discord link]
|-
|style="text-align:center" |Andrew Ducharme
|872,041
|784,099
|10.1%
|456.4
|0.0535
|0.5034
|style="text-align:left" |Enumerate.py w/ 250k max-loops and block-mult=3 on <code>7x2_p01_s02_holdouts_rand_72.txt</code>
|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1403236957298884679 Discord link]
|-
|style="text-align:center" |Terry Ligocki
|1,000
|982
|1.8%
|3.3
|0.0015
|0.0830
|style="text-align:left" |[[MITMWFAR]] [https://github.com/Iijil1/MITMWFAR Code] with options <code>-n=10 -m=1 -pm=1</code> on the first 1,000 TMs in <code>7x2_p01_s03_holdouts_rand_47.txt</code>
|style="text-align:left" |
|-
|style="text-align:center" |Andrew Ducharme
|800,507
|693,348
|13.3%
|2818.7
|0.0106
|0.0789
|style="text-align:left" |Enumerate.py w/ 1M max-loops and block-mult=4 on holdouts from above Enumerate run on<code>7x2_p01_s02_holdouts_rand_72.txt</code>
|style="text-align:left" |
|-
|style="text-align:center" |Andrew Ducharme
|70,000
|65,615
|6.3%
|6.6
|0.1842
|2.9412
|style="text-align:left" |Enumerate.py with --no-sim and --lin-steps=100000 on <code>7x2_p01_s02_holdouts_rand_65.txt</code>
|style="text-align:left" |
|-
|style="text-align:center" |Terry Ligocki
|10,000
|various
|2% - 32%
|various
|various
|various
|style="text-align:left" |See the "Source" discussion on the discord channel which includes graphs with quantitative data. A parameter study of random sample of 10,000 TMs from the Phase 1, Stage 3 holdouts
|style="text-align:left" |[https://discord.com/channels/960643023006490684/1369339127652159509/1407090465097908245 Discord link]
|}
 
== Phase 2 ==
Phase 2 has now begun with Andrew Ducharme's initial decider run (see table below). The goal of Phase 2 is to run deciders on the current holdout list (the last in the table) and produce an accessible new holdout list which can then be added to the table. Accessing the holdout list can be done through the link in the "Source" column. If there isn't a link there it means the data is still being put somewhere everyone can access it.
 
{| class="wikitable sortable" style="text-align: right"
!rowspan="2" |Done by
!colspan="2" |Holdout TMs
!rowspan="2" |% Reduced
!rowspan="2" |Runtime (hours)
!colspan="2" |TMs/sec/core
!rowspan="2" |Description
!rowspan="2" |Source
|-
!Input
!Output
!Decided
!Processed
|-
|style="text-align:center" |Andrew Ducharme
|86,129,304
|82,226,951
|4.5%
|119.6
|9.0634
|200.04
|style="text-align:left" |CPS_Filter with --max-block-size=4
|style="text-align:left" |
|}
 
[[Category:BB Domains]]

Latest revision as of 06:52, 19 August 2025

The 7-state, 2-symbol Busy Beaver problem, BB(7), refers to the unsolved 7th value of the Busy Beaver function. With the compilation of the Cryptid machine Bigfoot into a 7-state, 2-symbol machine in May 2024, we now know that we must solve a Collatz-like problem in order to solve BB(7).

The current BB(7) champion 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) was discovered by Pavel Kropitz in May 2025, proving the lower bound:

History

Before 2025, the only known BB(7) champions were produced by hand, not by search. In 1964, Milton Green designed a machine that had sigma score 22,961. In 2014, Wythagoras modified a BB(6) champion to produce a machine that had sigma score .

In May 2025, mxdys shared C++ code that breaks up the BB(7) enumeration into 1 million subtasks which each run for about 2 minutes and leave ~100 holdouts each. Various folks on Discord have been investigating different sections of this domain to search for champions.

Within three days of the code's release, the Ligockis found three champions after applying their deciders to enumerator output. Shawn Ligocki found the first two, 1RB0RF_1LC0RE_1RD1LB_1LA1LD_0RA0LE_1RG0LB_1RZ1RB (bbch) and 1RB1RA_1RC0LC_0LD1LG_1LF0LE_1RZ1LF_0LA1LD_1RA1LC (bbch), with sigma scores of approximately 10 ↑↑ 22 and 10 ↑↑ 35. That evening, Terry Ligocki found 1RB0LG_1RC0RF_1LD1RZ_1LF0LE_1RA1LD_1LG1RE_0LB0LB (bbch), with sigma score ~10 ↑↑ 46. A few days later, Pavel found a TM that outpaces all of them.

Pavel's champion is enumerated in subtask 243308.

Cryptids

BB(7) has not been seriously investigated by hand, so no native BB(7) Cryptids have yet been discovered.

Probviously non-halting Cryptids:

0RB1RB_1LC0RA_1RE1LF_1LF1RE_0RD1RD_1LG0LG_---1LB (bbch), Bigfoot (a BB(3,3) Cryptid) compiled into a 2-symbol TM by Iijil in 2024.

Top Halters

The top 20 scoring known machines are:

TM Approximate sigma score Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Andrew Ducharme
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Andrew Ducharme
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE (bbch) 10 ↑↑ 519.20 @gerbil5709, Terry Ligocki
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32 @Iijil
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA (bbch) 10 ↑↑ 246.32 @star, Terry Ligocki
1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch) 10 ↑↑ 243.88 @Iijil, Andrew Ducharme
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch) 10 ↑↑ 228.78 Terry Ligocki
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_0RG0LA_1RB1RZ (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RD0LA_1RF0RA_1RG0LA_0LE1RZ (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RG0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LG_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RC0LD (bbch) 10 ↑↑ 192.67 Andrew Ducharme
1RB1LA_1LC0RE_0LD1LB_1RE1LG_1RF0LG_0RA0LA_0RF1RZ (bbch) 10 ↑↑ 192.67 Andrew Ducharme
1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch) 10 ↑↑ 192.67 @C7X
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch) 10 ↑↑ 192.67 @Iijil, Terry Ligocki
1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_1RG0LA_0LE1RZ (bbch) 10 ↑↑ 192.67 @Iijil, Terry Ligocki

The top 20 known halters with unique scores are:

TM Approximate sigma score Discoverer
1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch) Pavel Kropitz
1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Andrew Ducharme
1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Terry Ligocki
1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32 @Iijil
1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch) 10 ↑↑ 243.88 @Iijil, Andrew Ducharme
1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch) 10 ↑↑ 228.78 Terry Ligocki
1RB1RZ_1LC0RE_0LD1LB_1RE0LA_1RF0RG_0RA0LG_1RB1LG (bbch) 10 ↑↑ 192.67 Terry Ligocki
1RB0LC_1LC1LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Terry Ligocki
1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch) 10 ↑↑ 140.28 @stokastic
1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA (bbch) 10 ↑↑ 136.64 Katelyn Doucette, Andrew Ducharme
1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch) 10 ↑↑ 133.85 @poppuncher
1RB1RZ_1RC0RF_1LD1RB_1RG0LE_1LD0RA_1RE0LD_0RC1LF (bbch) 10 ↑↑ 129.24 @Iijil
1RB0RG_1LC0RE_1LF1LD_0LE1LC_1RA1RB_1LD0LF_1RZ0RF (bbch) 10 ↑↑ 127.52 Andrew Ducharme
1RB0LC_1RC0RG_1RD0LF_1RE0RF_1LA1RG_1LE1LF_1RZ1RD (bbch) 10 ↑↑ 126.20 @stokastic
1RB0LD_1RC1RA_0RD1RG_1LE1LF_0LF1LE_0RA0LD_0RA1RZ (bbch) 10 ↑↑ 124.86 Terry Ligocki
1RB1LF_1RC1RA_1LD0LD_1LA1LE_0LA0LD_1LG0RF_0LE1RZ (bbch) 10 ↑↑ 116.98 Terry Ligocki
1RB0RD_1RC0LA_0LA0LE_1RE1RZ_1RF0RA_1LG0LE_1LC0LG (bbch) 10 ↑↑ 116.05
1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch) 10 ↑↑ 115.52 @prurq
1RB0RG_1LC0LE_1LD0LB_0LE1RE_0RA1RF_0RD1RC_1RD1RZ (bbch) 10 ↑↑ 114.83 Andrew Ducharme
1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch) 10 ↑↑ 114.60 Shawn Ligocki

Phase 1

Phase 1's first two stages were carried out from May 2025 to July 2025. The table below summaries some of that activity and was used to coordinate the effort of doing the raw computation. Fourteen people (see below) contributed directly and the overall bbchallenge group participated in discord discussions, etc.

Stage 1, "enumeration" in the table, involved running 1 million subtasks using mxdys's code in 100 batches of 10 thousand subtasks.

Stage 2, "linear rule" in the table, processing the output of Stage 1 using Shawn Ligocki's linear rule code which also used a few other deciders, e.g., a version of CTL.

Stage 3, the final stage of Phase 1, is the compilation, verification, and presentation of the final results from Phase 1. It is ongoing but should be completed during August 2025.

Task range Done by Completed # holdouts Maximum Score TM ~Sigma Source
enumeration linear rule
00-01xxxx @Iijil Yes Yes 1,545,673 1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA0LG_1RZ0RD (bbch) 10 ↑↑ 246.32 Google Drive folder
02-04xxxx

@Iijil
Terry Ligocki

Yes Yes 2,279,734 1RB0LF_1RC1RA_1RD0RG_1LE1RZ_1LA0LF_1RA1LE_0RE1RG (bbch) 10 ↑↑ 93.81

@Iijil
Terry Ligocki

05-09xxxx

@Iijil
Andrew Ducharme

Yes Yes 3,889,955 1RB1RZ_1RC0LE_0RD1RB_1LE1RA_1LF0LG_0LG0RG_1LB1RG (bbch) 10 ↑↑ 243.88

@Iijil
Andrew

10-12xxxx Andrew Ducharme Yes Yes 2,708,888 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Google Drive folder
13xxxx Shawn Ligocki Yes Yes 1,192,442 1RB0RE_1LC0LA_1LD0LC_0LE0LA_1RF0RG_1RD0LE_1RA1RZ (bbch) 10 ↑↑ 114.60 Google Drive folder
14-16xxxx Andrew Ducharme Yes Yes 2,701,637 1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0LD_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Google Drive folder
17-18xxxx

@gerbil5709
Terry Ligocki

Yes Yes 1,898,156 1RB1LA_1LC0RE_0LD1LB_1RE0LA_1RF0RA_0RG0LA_1RB1RZ (bbch) 10 ↑↑ 192.67

@gerbil5709
Terry Ligocki

19xxxx

Katelyn Doucette
Andrew Ducharme

Yes Yes 1,099,752 1RB0RF_1RC1RZ_0LD1RF_0RA1LE_0LC1LF_1LE0RG_0LE1RA (bbch) 10 ↑↑ 136.64 Google Drive folder
20-23xxxx @C7X Yes Yes 4,528,827 1RB1LA_1LC0RF_0LD0RD_1RF1LE_1LB1RZ_1RG0RA_0RA0LA (bbch) 10 ↑↑ 192.67 Google Drive folder
24xxxx Andrew Ducharme Yes Yes 712,356 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* Google Drive folder
25-34xxxx @stokastic Yes Yes 10,339,816 1RB0LC_1LC0LD_1LA1LB_0LG1RE_1LD0RF_0RA1RE_1RZ1LC (bbch) 10 ↑↑ 140.28 Google Drive folder
35-39xxxx Terry Ligocki Yes Yes 4,894,047 1RB1RZ_1LC0RF_0LD1LB_1RD0LE_1RB1LE_1RG0RE_0RA0LE (bbch) 10 ↑↑ 192.67 Google Drive folder
40-47xxxx Andrew Ducharme Yes Yes 6,181,327 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LF_0RD1LF_1LB0LE (bbch) 10 ↑↑ 519.20 Google Drive folder
48xxxx

@star
Terry Ligocki

Yes Yes 727,875 1RB0LE_1RC0RA_1RD0RC_1LE1LD_1LA0LF_0LA1LG_1RZ1LA (bbch) 10 ↑↑ 246.32

@star
Terry Ligocki

49xxxx

Tobiáš Brichta
Terry Ligocki

Yes Yes 804,722 1RB0LG_1RC0RG_0LD1RE_1RD0RE_1LF1RB_0LA1RZ_1LC1LG (bbch) 10 ↑↑ 126.20

Tobiáš Brichta
Terry Ligocki

50xxxx

@prurq
Andrew Ducharme

Yes Yes 797,224 1RB0RD_1RC0RA_0RD1LD_0LE1LF_1LA0LG_0LC1LB_1LC1RZ (bbch) 10 ↑↑ 115.52 Google Drive folder
51-53xxxx

@gerbil5709
Terry Ligocki

Yes Yes 3,016,175 1RB0LC_1LC0LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LC (bbch) 10 ↑↑ 140.28

@gerbil5709
Terry Ligocki

54-59xxxx Terry Ligocki Yes Yes 5,689,850 1RB0LC_1LC1LD_1LA1LB_0LG1RE_0RF0RF_0RA1RE_1RZ1LA (bbch) 10 ↑↑ 188.28 Google Drive folder
60-64xxxx

@gerbil5709
Terry Ligocki

Yes Yes 3,817,876 1RB1RZ_0RC0RE_1LD1LA_1LC0LG_0RF1LE_0RD0LG_1LB0LE (bbch) 10 ↑↑ 519.20

@gerbil5709
Terry Ligocki

65-68xxxx Terry Ligocki Yes Yes 3,076,778 1RB0LD_0LC1RZ_1RA0RD_1RE1LD_1LF0RC_0LG1LE_1RG0LD (bbch) 10 ↑↑ 192.67 Google Drive folder
69xxxx @poppuncher Yes Yes 1,053,119 1RB0LG_0RC1RZ_1LD0LA_1RE1LE_1LC1RF_0RE0RA_0RF1LG (bbch) 10 ↑↑ 133.85 Google Drive folder
70-71xxxx @hipparcos Yes Yes 1,899,094 1RB1RZ_1LC1RD_0LD0LC_1LE1RA_1LF0LE_1RF0RG_1RG0RD (bbch) 10 ↑↑ 77.50 Github release
72-79xxxx Terry Ligocki Yes Yes 7,627,514 1RB0RB_1LC1RG_1RD1RC_1RE0RA_1LF0LB_1RF0LE_0RD1RZ (bbch) 10 ↑↑ 228.78 Google Drive folder
80-81xxxx @xnoobspeakable Yes Yes 1,537,533 1RB0LA_0RC1RZ_0RD0RG_1LE1RA_1LF1LD_1RG0RG_1RD1RC (bbch) 10 ↑↑ 74.85 Google Drive folder
82-99xxxx Terry Ligocki Yes Yes 15,673,786 1RB1RF_0RC1RG_1LD1LE_0LE1LD_0RF0LC_1RA0LC_0RF1RZ (bbch) 10 ↑↑ 286.17 Google Drive folder

*The current BB(7) champion TM 1RB0RA_1LC1LF_1RD0LB_1RA1LE_1RZ0LC_1RG1LD_0RG0RF (bbch)* was discovered by Pavel Kropitz in the enumeration of subtask 243308. The remaining subtasks in the 24xxxx range were enumerated and filtered by Andrew Ducharme.

Exploration after Phase 1

People are now looking at reducing the number of holdouts (~85M TMs) after Phase 1. They are trying different deciders not used in Phase 1 and different parameters with the deciders used in Phase 1. This table is somewhere they can put the results of these explorations so that there is a record of what is being done. It is hoped that this will inspire everyone to contribute when they can, a reference point for discord discussions, and something that can be questioned and/or verified.

Done by Holdout TMs % Reduced Runtime (hours) TMs/sec/core Description Source
Input Output Decided Processed
Shawn Ligocki 858,538 733,830 14.5% 5.0 6.9282 47.6966 Translated Cycler and CPS on 7x2_p01_s02_holdouts_rand_13.txt Discord link
Andrew Ducharme 872,041 784,099 10.1% 456.4 0.0535 0.5034 Enumerate.py w/ 250k max-loops and block-mult=3 on 7x2_p01_s02_holdouts_rand_72.txt Discord link
Terry Ligocki 1,000 982 1.8% 3.3 0.0015 0.0830 MITMWFAR Code with options -n=10 -m=1 -pm=1 on the first 1,000 TMs in 7x2_p01_s03_holdouts_rand_47.txt
Andrew Ducharme 800,507 693,348 13.3% 2818.7 0.0106 0.0789 Enumerate.py w/ 1M max-loops and block-mult=4 on holdouts from above Enumerate run on7x2_p01_s02_holdouts_rand_72.txt
Andrew Ducharme 70,000 65,615 6.3% 6.6 0.1842 2.9412 Enumerate.py with --no-sim and --lin-steps=100000 on 7x2_p01_s02_holdouts_rand_65.txt
Terry Ligocki 10,000 various 2% - 32% various various various See the "Source" discussion on the discord channel which includes graphs with quantitative data. A parameter study of random sample of 10,000 TMs from the Phase 1, Stage 3 holdouts Discord link

Phase 2

Phase 2 has now begun with Andrew Ducharme's initial decider run (see table below). The goal of Phase 2 is to run deciders on the current holdout list (the last in the table) and produce an accessible new holdout list which can then be added to the table. Accessing the holdout list can be done through the link in the "Source" column. If there isn't a link there it means the data is still being put somewhere everyone can access it.

Done by Holdout TMs % Reduced Runtime (hours) TMs/sec/core Description Source
Input Output Decided Processed
Andrew Ducharme 86,129,304 82,226,951 4.5% 119.6 9.0634 200.04 CPS_Filter with --max-block-size=4
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