Proof Sought: B34/S23-ish still lifes

[Tropylium]

Rules that are approximately B34/S23, possibly with some additional higher-end birth/survival conditions (B7, B8, S7, S8), have the interesting trait that they allow still lifes — but only a seemingly finite variety. (Life-like rules of this family are explosive in character, but in Generations they're often stabilizing.) The only still lifes I have been able to find are:
• block
• boat
• beehive
• ship
• long ship
And, indeed, look at any larger GoL still life, and there is always an A4 cell somewhere.

It's simple to prove that pseudo still lifes or induction coil still lifes are impossible in these rules: the pseudo or coil division line cannot jump straight from A5 to A2, without passing thru B3 or B4, since all adjacent cells on the division line share 4 of their neighbors. This also shows that a still life cannot have concavities that squeeze thru an opening. But this logic does not seem to rule out still lifes with a mostly convex outline, along the lines of bi-beehive or big beehive.

Infinite stable wicks are possible as well, even:

Code: Select all

x = 41, y = 41, rule = 23/34/3
39.A$37.3A$36.A3.A$35.A.3A$35.A.A$33.3A.A$32.A3.A$31.A.3A$31.A.A$29.
3A.A$28.A3.A$27.A.3A$27.A.A$25.3A.A$24.A3.A$23.A.3A$23.A.A$21.3A.A$
20.A3.A$19.A.3A$19.A.A$17.3A.A$16.A3.A$15.A.3A$15.A.A$13.3A.A$12.A3.A
$11.A.3A$11.A.A$9.3A.A$8.A3.A$7.A.3A$7.A.A$5.3A.A$4.A3.A$3.A.3A$3.A.A
$.3A.A$A3.A$.3A$.A!

But they do not seem to be stabilizable into finite still lifes.