TMBR: October 2025: Difference between revisions

Latest revision as of 20:58, 28 October 2025

Prev: September 2025	This Month in Beaver Research	Next: November 2025

This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).

TODO: BB(3x3) month

A brave busy beaver confronts the dreaded Antihydra. Copyright Nico Roper.

Misc

TODO: Add the mechanical Turing Machine. discord source: https://discord.com/channels/960643023006490684/1362008236118511758/1425889021653160026 and onwards

TODO: Add the method used by @Bricks to measure susceptibility to block-analysis. discord source: https://discord.com/channels/960643023006490684/1239205785913790465/1430227817957953638 also results: https://docs.google.com/spreadsheets/d/1j00LBxxp9W7uz1wZdMIvDCZ56eReuH0IGO9Z8-yybcQ/edit?usp=sharing

Blog Posts

22 Oct 2025. Ben Brubaker. Why Busy Beaver Hunters Fear the Antihydra.
? Oct 2025. Katelyn Doucette. Building the Busy Beaver Ladder.

Champions

BB(4,3):
- Polygon analysed the remaining potential champions discovered by Pavel Kropitz in May 2024, discovering that 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch) is the new BB(4,3) champion with a score of over $10 ↑^{4} 4$ .

Holdouts

BB Holdout Reduction by Domain
Domain	New Holdout Count	Previous Holdout Count	Holdout Reduction	% Reduction
BB(6)	1618	1691	73	4.3%
BB(7)	20,405,295	22,801,601	2,396,306	10.5%
BB(4,3)	9,401,447	460,916,384	451,514,937	98.0%
BB(3,4)	15,136,283	434,787,751	419,651,468	96.6%
BB(2,6)	870,085	873,469	3384	0.4%

BB(6):
- @mxdys shared a new holdouts list on October 20th, consisting of 1618 machines up to equivalence, or 3067 individual machines. This means 73 newly solved machines, a 4% reduction.
- @Bricks shared a machine which they thought could be susceptible to block-analysis based on a method they call Subtape Saturation Heuristic. Shawn Ligocki's analysis, simulated by @Bricks showed the machine to halt with a sigma score of 4,419,340,317.
- Analysis by Racheline showed a machine to be non-halting.
BB(7):
- Andrew Ducharme has continued reducing the number of holdouts with Stage 4 of Phase 2. Afterwards, Terry Ligocki ran Stage 5 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 20,405,295 holdouts remain. (10.51% reduction)
BB(4,3):
- Terry Ligocki has begun Phase 2 of holdout reduction, reducing the number of holdouts from 460,916,384 to 9,401,447. (97.96% reduction)
BB(3,4):
- XnoobSpeakable and Lúkos are running filters in the domain under Phase 2, reducing the holdout count from 434,787,751 to 15,136,283. (96.6% reduction)
BB(2,5):
- Peacemaker II gave an informal proof of a machine never halting, making the informal holdout count 64.
BB(2,6):
- Andrew Ducharme has completed Stage 3 of Phase 2, reducing the number of holdouts from 873,469 to 870,085. (0.39% reduction)

Theory

Piecewise Affine Functions (PAF) were explored as a generalization of the BMO1 rules:

@Bard proved that 3 dimension PAF are Turing complete: [1]
@star proved that 2 dimension PAF are Turing complete: [2]
Shawn Ligocki wrote up a proof sketch that 2-region PAF are Turing complete: [3]
It was discovered that Amir Ben-Amram had already proven that 2-dim and 2-region PAF were Turing complete in 2015.
BMO1 is a 2-dim, 2-region PAF so this provides some sense for the difficulty of the problem.

Deciders

TODO: Add -d's cpp quick_sim project. Discord source: https://discord.com/channels/960643023006490684/1226543091264126976/1426265937455222794

TODO: Add Katelyn's inductive project. Discord source:https://discord.com/channels/960643023006490684/1369339127652159509/1419016459560161280 https://discord.com/channels/960643023006490684/1095740122139480195/1427714010697961534

@@ Line 1: / Line 1: @@
 {{TMBRnav|September 2025|November 2025}}''This edition of TMBR is in progress and has not yet been released. Please add any notes you think may be relevant (including in the form a of a TODO with a link to any relevant Discord discussion).''
+TODO: BB(3x3) month
 [[File:Nico-BB-vs-Antihydra.jpg|thumb|A brave busy beaver confronts the dreaded Antihydra. Copyright [https://www.nicoroper.com/ Nico Roper].]]
@@ Line 15: / Line 17: @@
 * [[BB(4,3)|BB(4,3):]]
-**Polygon analysed the remaining "potential champions" discovered by Pavel Kropitz in May 2024, discovering that {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}} is the new BB(4,3) champion with a score of over <math>10 \uparrow^{4} 4</math>.
+**Polygon analysed the remaining [[BB(4,3)#Potential Champions|potential champions]] discovered by Pavel Kropitz in May 2024, discovering that {{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}} is the new BB(4,3) champion with a score of over <math>10 \uparrow^{4} 4</math>.
 == Holdouts ==
+[[File:BB(6) holdouts decrease over time.png|alt=BB(6) Holdouts count decrease overtime.|thumb|BB(6) Holdouts count decrease overtime.]]
+{| class="wikitable"
+|+BB Holdout Reduction by Domain
+!Domain
+!New Holdout Count
+!Previous Holdout Count
+!Holdout Reduction
+!% Reduction
+|-
+|[[BB(6)]]
+|1618
+|1691
+|73
+|4.3%
+|-
+|[[BB(7)]]
+|20,405,295
+|22,801,601
+|2,396,306
+|10.5%
+|-
+|[[BB(4,3)]]
+|9,401,447
+|460,916,384
+|451,514,937
+|98.0%
+|-
+|[[BB(3,4)]]
+|15,136,283
+|434,787,751
+|419,651,468
+|96.6%
+|-
+|[[BB(2,6)]]
+|870,085
+|873,469
+|3384
+|0.4%
+|}
 * [[BB(6)|BB(6):]]
 ** @mxdys [https://discord.com/channels/960643023006490684/1239205785913790465/1429892916763033601 shared a new holdouts list on October 20th,] consisting of 1618 machines up to equivalence, or 3067 individual machines. This means 73 newly solved machines, a 4% reduction.
@@ Line 24: / Line 64: @@
 ** [https://discord.com/channels/960643023006490684/1239205785913790465/1431225455557611611 Analysis by Racheline] showed a machine to be non-halting.
 * [[BB(7)|BB(7):]]
-** Andrew Ducharme has continued reducing the [[BB(7)#Phase 2|number of holdouts]] with Stage 4 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 22,721,168 holdouts remain. (0.35% reduction)
+** Andrew Ducharme has continued reducing the [[BB(7)#Phase 2|number of holdouts]] with Stage 4 of Phase 2. Afterwards, Terry Ligocki ran Stage 5 of Phase 2. Initially, in the beginning of the month there were 22,801,601 holdouts, and 20,405,295 holdouts remain. (10.51% reduction)
 * [[BB(4,3)|BB(4,3):]]
-**Terry Ligocki has begun [[BB(4,3)#Stage 2|phase 2 of holdout reduction,]] reducing the number of holdouts from 460,916,384 to 9,401,447. (97.96% reduction)
+**Terry Ligocki has begun [[BB(4,3)#Phase 2|Phase 2 of holdout reduction,]] reducing the number of holdouts from 460,916,384 to 9,401,447. (97.96% reduction)
 *[[BB(3,4)|BB(3,4):]]
 **[[User:XnoobSpeakable|XnoobSpeakable]] and [[User:WarpedWartWars|Lúkos]] are running filters in the domain under [[BB(3,4)#Phase 2|Phase 2]], reducing the holdout count from 434,787,751 to 15,136,283. (96.6% reduction)
 *[[BB(2,5)|BB(2,5):]]
-**[https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437 Peacemaker II gave an informal proof of a machine never halting], making the informal holdout count 67.
+**[https://discord.com/channels/960643023006490684/1259770421046411285/1428501877947109437 Peacemaker II gave an informal proof of a machine never halting], making the informal holdout count 64.
 *[[BB(2,6)|BB(2,6):]]
-**Andrew Ducharme has completed [[BB(2,6)#Stage 3|stage 3 of phase 2]], reducing the number of holdouts from 873,469 to 870,085. (0.39% reduction)
+**Andrew Ducharme has completed [[BB(2,6)#Stage 3|Stage 3 of Phase 2]], reducing the number of holdouts from 873,469 to 870,085. (0.39% reduction)
 == Theory ==
-TODO: Update this section after studying existing literature a bit more.
+[[Piecewise Affine Function|Piecewise Affine Functions]] (PAF) were explored as a generalization of the [[BMO1]] rules:
-[[Linear-Inequality Affine Transformation Automata]] (LIATA) were introduced as a generalization of the [[BMO1]] rules:
-* @Bard proved that 3 dimension LIATA are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1420457986564030641]
+* @Bard proved that 3 dimension PAF are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1420457986564030641]
-* @star proved that 2 dimension LIATA are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1421271424588451915]
+* @star proved that 2 dimension PAF are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1421271424588451915]
-* BMO1 is a 2d-LIATA so this provides some sense for the difficulty of the problem.
+* Shawn Ligocki wrote up a proof sketch that 2-region PAF are Turing complete: [https://discord.com/channels/960643023006490684/1239205785913790465/1422772752980639866 <nowiki>[3]</nowiki>]
+* It was discovered that Amir Ben-Amram had already proven that 2-dim and 2-region PAF were Turing complete in 2015.
+* BMO1 is a 2-dim, 2-region PAF so this provides some sense for the difficulty of the problem.
 == Deciders ==

TMBR: October 2025: Difference between revisions

Latest revision as of 20:58, 28 October 2025

Contents

Misc

Blog Posts

Champions

Holdouts

Theory

Deciders

Navigation menu

TMBR: October 2025: Difference between revisions

Latest revision as of 20:58, 28 October 2025

Misc

Blog Posts

Champions

Holdouts

Theory

Deciders

Navigation menu

Search