User talk:H. H. P. M. P. Cole/ConwayLife 2050

Conjectures that are too easy

Shouldn't

“ A smaller unsynthesizable SL is created ”

have a criterion like an upper bound for its population or number of specified cells? You last edited it on March 1, and it was reduced from 278 to 236 on March 12.

“ A finite set of synth components is found and proven complete for all synthesizable SLs. ”

seems to require clarification; if by a component you mean a stabilised subsection of a still life and set of initial positions for gliders relative to it, in which case (excluding RCTs) it is equivalent to the statement

“ there is a pair of constants c₀,c₁, such that for any synthesisable still life, there exists a sequence of constellations (with the last being the still life itself), such that a set of ≤ c gliders may be added around the nth member to produce the n+1th, whose effect is constrained to a c₁ × c₁ bounding box. ”

which seems nontrivial to me, and might warrant addition to the list of open problems. (The c₀ part is implied by c₁ but not sufficient on its own, since every synthesisable still life has a 1-glider seed. The known seed constructions would be prevented by the additional constraint of being still lifes rather than constellations, but it may be possible to attach each component of the seed to a piece of scaffolding to deconstruct later, c₁ prevents this.)

“ SKOP gets permanent upper bound of ≤ 104 ”

The current maximal-population SKOP of any period is the 228-cell p67 Snark loop, but if you meant an upper bound for all periods ≤ a constant, Skopje's readme notes a construction yielding an upper bound of 141 for all periods ≤ 187, which can be improved to ≤ 104 by the specific cases up to it (following the 180-cell p103 mentioned in the current adjustable glider loop page). DroneBetter (talk) 20:48, 20 April 2024 (UTC)

• Thanks for the suggestions, DroneBetter!

1. I currently want the smallest unsynthesizable SL to have less than 136 cells, coincidentally 100 cells smaller than the current smallest unsynthesizable SL.

2. Your version of the conjecture is superior to mine, so I changed the conjecture and credited you.

3. I meant that the minpop of all SKOPs would be proven (by 2050) to be less than 104, and I changed the wording in the page to reflect that.

H. H. P. M. P. Cole - the factorialship's owner (talk) 00:38, 21 April 2024 (UTC)