TMBR: September 2025

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Revision as of 18:28, 28 September 2025 by Sligocki (talk | contribs) (→‎Holdouts: Add citation links, cleanup and expand description of various holdout items.)
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This Month in Beaver Research for September 2025.

TODO: BB(5) arXiv released https://arxiv.org/abs/2509.12337

TODO: BB(3,3) month next month.

In the News

Blog Posts

Holdouts

This month saw huge reductions to holdout lists in many domains. In BB(6), this was mainly due to mxdys demonstrating the equivalence of many TMs. For the other domains it seems to be mainly due to applying mxdys's main.exe and the Ligockis' Enumerate.py and lr_enum_continue decider pipelines to these domains.

BB Holdout Reduction by Domain
Domain New Holdout Count Previous Holdout Count Holdout Reduction % Reduction
BB(6) 1,691 2,592 901 34.8%
BB(7) 23,314,388 59,727,905 36,413,517 61.0%
BB(2,6) 873,469 22,302,296 21,428,827 96.1%
BB(4,3) 97,701,052 460,916,384 363,215,332 78.8%
  • BB(6):
    • Equivalence Classes:
      • @mxdys shared a new way of grouping TMs by equivalence class, this reduced the number of holdout equivalence classes from 2467 to 1691 (31% reduction).
      • There is some debate about what precisely defines a holdout. Should it be the full list of TNF TMs that are undecided? Or should it be a list of one TM per equivalence class or in other words, a list of TMs such that solving them will also solve all remaining TMs (due to behavioral equivalence). In practice, most holdouts list involve some amount of trimming for equivalence classes whether that is by using TNF-1RB or Marxen-style pruning. For consistency with previous holdouts lists, we list the number of equivalence classes as the holdout count above.
      • @mxdys published a list of 3171 total individual holdout TMs across the 1691 equivalence classes.
    • Andrew Ducharme and @mxdys both found a family of 10 halting TMs independently, all halting in around steps.
    • @mxdys decided two machines’ fates from the 50 Random Holdouts released in August, making 8/50 machined solved as of this month.
    • Andrew Ducharme (with help from Peacemaker II) found 3 additional halting TMs: 1 2 3.
  • BB(7):
    • Andrew Ducharme has continued reducing the number of holdouts, from 59,727,905 to 28,189,617 (52.80% reduction).
    • Terry Ligocki ran an additional 41 filters/parameters. This reduced the number of holdouts, from 28,189,617 to 23,314,388 TMs (17.29% reduction)
  • BB(2,6):
    • @Peacemaker II noticed some TMs missing from Andrew Ducharme reductions. It was decided to start back at the original 22,302,296 holdout TMs.
    • Andrew Ducharme ran lr_enum_continue and reduced the 22,302,296 holdout TMs to 20,358,011 (8.72% reduction).
    • Terry Ligocki ran 50 variations of deciders/parameters using @mxdys' C++ code, main.exe, reducing the holdout count to 970,101 TMs (95.23% reduction)!
    • Andrew Ducharme ran Enumerate.py reducing the holdout count to 873,469 TMs (9.96% reduction).
  • BB(4,3):
    • Terry Ligocki ran a set of deciders/parameters from @mxdys' code to reduce the number of holdouts which were at 460,916,384 TMs. Six passes have reduced the holdout count to 97,701,052 TMs (78.80% reduction). (TODO: Source)
  • BB(3,4):
    • TODO: XnoobSpeakable and Lúkos are working on the holdout list for BB(3,4), ~435M TMs, using @mxdys' deciders with various parameters.

BB Adjacent

  • John Tromp announced on Discord that a 350-bit function now reaches the limit of BMS, an improvement from the previous 404 bits.

TODO: phrasing. Discord source: https://discord.com/channels/960643023006490684/1355653587824283678/1413637783045542038 and https://github.com/tromp/AIT/blob/master/fast_growing_and_conjectures/bms.lam

Misc

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