This post summarizes a family of 5 decider holdouts (proved infinite by hand).
They are:
1RB0LE_1RC1RB_1RD1LC_0LE0RB_---1LA= 7763480 proof1RB1RA_1RC1LB_0LD0RA_1RA1LE_---0LD= 8120967 proof1RB1RE_1LC1RB_0RA0LD_1LB1LD_---0RA= 10756090 proof1RB1LA_0LC0RE_---1LD_1RA0LC_1RA1RE= 11017998 proof1RB1LA_0LC0RE_---1LD_1LA0LC_1RA1RE= 11018487 proof
Years ago, Skelet noticed them and wrote: " N_2N and 3N machines are 3-linear sequences, but with little complex behavior than the machines, proved by methods TryL1Cnt and TryModFin. They are easy provable by hand." (“N_2N” corresponds to these five; “3N” corresponds to a holdout family I’ve called “helix”.)
I called them “finned” cubic machines when I noticed them as CTL holdouts.
They are provably CTL holdouts, as illustrated by @Iijil: 10756090 is irregular.
Analysis has shown they’ll likely remain holdouts for any Weighted Finite Automata decider (using a single integer weight): a closed language of configs can be described in this way (and the linked proofs effectively do that), but the transitions do not vary the weights smoothly.
However, @mxdys has reported being able to extend a Repeated-Word List CTL decider in a way that allows linear equalities between repeater counts, and it was effective at solving these machines.
@meithecatte has also at least started to explore automatic deciders that could cover this class
Therefore, these machines may soon lose their status as special cases.