I am of course incapable of impartiality, but will give as full a chronology as I can.
- No later than 2001-01-14: David Eppstein creates a page in his page, "Replicators: B36/S245"
- 2009-08-07: apg adds this to the Gun LifeWiki page, under the name "Logarithmic replicator rule"
- 2018-12-17: Muzik creates a page on the wiki under the same name, redirecting to Eppstein's page
- 2019-06-02: Ian07 turns this into a then-stubby, but full-fledged page of its own.
- 2019-06-26, 2020-04-12 (AforAmpere finds a 3-cell-wide pattern in an INT rule, emulating the replicator), 2020-08-19, 2021-05-22, 2021-10-21, 2022-09-25: Various uses of the name "Logarithmic replicator rule" appear in the forums
- 2023-09-29 (talk page): I find exact forms (in terms of bitwise and special functions) for the functions that give the number of iterations for the left and right edges to reach specific distances from the origin, in AforAmpere's emulator (equivalent to the 4-state Wolfram rule 0x190e002061040c0b86d0010e5980). This provides that the cell-length in the t'th iteration, l(t), has the asymptotic bounds 2*√t < l(t) < 2*√(5*t/3). As such, this prevailing name is incorrect, since the replicator's asymptotic width is Θ(√t).
- 2023-09-30 (Tiki bar), 2023-10-21 (my talk page): Disagreement ensues
At present, the name of the page is "OCA:Logarithmic replicator rule" and the replicator embed is labelled "The namesake logarithmic replicator," yet my result is shown in the section OCA:Logarithmic replicator rule#Growth_bounds.
At present, for the page's title, we have three main options before us:
1. Leave it as-is forevermore (this is incorrect, but retains consistency with the many existing mentions. Proposed by Confocal)
2. Move it to "OCA:B36/S245" (more clinical, doesn't note the reason for its interestingness. Proposed by Galoomba)
3. Move it to "OCA:sqrt replicator rule" or (in keeping with O(sqrt(log(t)))) "OCA:Θ(√t) replicator rule" (Proposed by me)
Note that an administrator could also go through and amend all past mentions of the rule in the forums, probably negating the advantage of option 1.
If anyone has any opinions, they may express them here, with the intention of coming to a consensus in a civil (albeit perhaps arbitrarily protracted :-) manner, that doesn't involve any back-and-forth deleterious sparring edits.