TMBR: November 2026

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This Month in Beaver Research

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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).

This Month in Beaver Research for November 2026.

BB Adjacent

• Pebble Automaton
  • On November 2, User:AlephSquirrel found the golems, a group of 22 pebble(11) holdouts modeled by complex systems of equations, making them potential cryptids. They can be categorized into 7 unique paths.

Champions

New champions discovered this month

Domain	Champion	Discoverer	New lower bound	Discoverer	Previous lower bound
BB(20)	1RR---_0LJ0RC_1RB1LD_0LD1LE_1LF1RG_1LI0LE_0RE1LD_1RB1RH_1RH1RN_1LK1LJ_0LL1LJ_1RM1RA_0RM0RH_0LO1RN_1LP0LP_1RH1LQ_1LO1LO_1LS1RR_1RZ1LT_0LH0LS (bbch)	User:Jacobzheng	$f_{\omega +7}^2(5)$	User:Jacobzheng	$f_{\omega +6}^2(4)$
BB(11,4)	1RG3LB1RZ2RA_2LD---1LD2RA_3RB1LB3LC2RC_3RE---3LC2RC_---3RE3LH2LF_3RF2RF2LE1LF_2LC3LH2LJ2RG_---3RH1LI2RG_3RH1LH3LI2RI_------3LJ3RK_------2RA3RK (bbch)	User:Loader3229	$f_{\omega \cdot 2}(21)$		$f_{\omega +3}^2(4)$
BB(8,5)	2RG3LB4LC2RA4LB_1RZ---1LD2RA4LD_3RB1LB3LC2RC4LC_3RE---3LC2RC3LC_---3RE4LE4LH4RB_4LE3LG3LB2RF4LG_2LH3RG1LH2RF2RA_3RG1LG3LH2RH4LH (bbch)		$f_{\omega \cdot 2+1}(93)$	User:Loader3229	$f_{\omega \cdot 2}(32)$
BB(4,6)	5LD3LB5LC2RA4LB4LC_1RZ3RB1LC2RA3RD0LA_3RB1LB3LC2RC4LC1RA_3RB0LA2LC4LD4LC4LD (bbch)		$f_{\omega +2}(29)$		$f_{\omega +1}(2{\uparrow }^{15}5)$
BB(5,6)	1LE3LB2LA2RA4LB5RA_1RZ3RB1LC2RA3RD4RA_3RB1LB3LC2RC4LC2LB_3RB0LA5LE4LD4LC4LD_4LC5LC0RE5LE1RE2RE (bbch)		$f_{\omega +3}(31)$
BB(6,6)	5RB3LB1RZ2RA4LB---_2LC3RB1LD2RA3LF---_3RB1LB3LC2RC4LC0LE_3RB3RD3LC2RC---3RE_5RC3RE1RB4LC------_5RB------1LF------ (bbch)		$f_{\omega *2}(36)$
BB(7,6)	2LG3LB1RZ2RA4LB---_4LG3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC---3RD_5RB3RE---4LC3LG5LE_5RB5RB---1LF---5LF_5LF---1LC1LG---5LG (bbch)		$f_{{\omega }^2}(5)$

• User:Loader3229 discovered an array of champions based on Kropitz's current BB(3,4) champion, demonstrating the following bounds:
  • On November 1, BB(8,5) > $f_{\omega \cdot 2+1}(93)$.^[1] and BB(11,4) > $f_{\omega \cdot 2}(21)$.^[2]
  • On November 2, BB(4,6) > $f_{\omega +2}(29)$, BB(5,6) > $f_{\omega +3}(31)$, BB(6,6) > $f_{\omega *2}(36)$ and BB(7,6) > $f_{{\omega }^2}(5)$.
• On November 2, User:Jacobzheng discovered a machine that demonstrates the lower bound BB(20) > $f_{\omega +7}^2(5)$.

Holdouts

BB Holdout Reduction by Domain

Domain	New Holdout Count	Previous Holdout Count	Holdout Reduction	% Reduction
BB(6)	608	608	0	0.00%

• BB(6)
  • On November 1, Ahmer Reza simulated two holdouts, both Reus Vampires, to halting.^[3]

Cryptids

All Turing machines mentioned in this section work with an alphabet of 2 symbols unless explicitly stated. The state bounds given also only consider Turing machines which work with 2 symbols.

• Cryptids in the Wild (+ Energy Vampires)
  • Reus Vampires
    • On November 1, Ahmer Raza ran path O4 to 1,941,376,761,248 iterations, at which point it halts!^[4] This path corresponds to a group of machines with halting times of over 10^{683,718,950,000} steps, and decides the last of the 7 Reus vampires.

• Larger Cryptids
  • Logical Independence
    • Zermelo-Frankel set theory
      • On November 1, charlie claimed to have used Claude to formally reduce the number of defined instructions required in a ZFC-independent TM to 375 (376 including the halting transition).
  • Computational Complexity Theory
    • On November 1, GregoryMorse claimed to have found a 278-state machine that quasihalts iff P = NP, a 295-state machine that quasihalts iff P = PP, and a 291-state machine that quasihalts iff P = PSPACE.^[5]

Other problems encoded into Turing machines this month

Conjecture	Domain	Discoverer	Discovery date	Notes
Pillai's conjecture	BBBB(91)	charlie, Claude[6]	November 1	Unknown - pseudoquasihalts if the conjecture is false. Proof.