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If the initial position of Conway's game of life is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Can we prove that such a vanishing is not possible for any $n>100$?

Edit: The sequence A061342 gives the period $p_n$ of the stationary component of the final pattern for an initial line of length $n$. But for $n \in [84,1000]$ we have $p_n \ge 2$, so the pattern must be non-vanishing in this case. But we observe (after Nathaniel Johnston) that for $n=500$, perpetual gliders are produced on the boundaries after $435$ steps, but $435<500$, so this must happens $\forall n \ge 500$.
It follows that the answer is yes.

Improved question: Is the stationary component non-vanishing for any $n > 1000$ ?

Stronger question: Is $p_n \ge 2$ for any $n > 1000$ ?

If the initial state of Conway's game of life is a line of $n \in [0,100]$ alive cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Is such a line non-vanishing for any $n \in [25,\infty)$?

Edit

Definition: a finite pattern $p$ has a weak period $wp$ if for any cell $c$ in the grid, there is $k>0$ such that the set of cells which are neighbours of neighbours of neighbours... ($k$ times) of $c$, is periodic of period $wp$ after sufficiently many generations, from the initial state $p$.

The sequence A061342 gives the weak period $wp_n$ of a line of $n$ alive cells. By combining the checking above with the fact that $wp_n \ge 2$ for $n \in [84,1000]$, we deduce that the pattern is non-vanishing for $n \in [25,1000]$. We observe that for $n=500$, four gliders are produced on the boundaries after $435$ steps, but $435<500$, so this must happens $\forall n \ge 500$. Assuming that these gliders (or others) are perpetual (as stated implicitly by Nathaniel Johnston in A061342, although without reference, while the proof could be non-trivial, as pointed out by Will Sawin in the comments), the answer to the above question would be yes.

Definition: a finite pattern $p$ is weakly-vanishing if any cell $c$ in the grid becomes perpetually dead after sufficiently many generations (depending on $c$), from the initial state $p$.

Improved question: Is there a weakly-vanishing line of $n$ alive cells with $n \in [25,\infty)$?

Stronger question: Is $wp_n \ge 2$ for any $[84,\infty)$ ?

Tobias Fritz pointed out in the comments that there is a one-cell thick pattern with infinite growth (see this page), but it is disconnected. Bonus question: Can that happen in the connected case?

If the initial position of Conway's game of life is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Can we prove that such a vanishing is not possible for any $n>100$?

Edit: The sequence A061342 gives the period $p_n$ of the stationary component of the final pattern for an initial line of length $n$. But for $n \in [84,1000]$ we have $p_n \ge 2$, so the pattern must be non-vanishing in this case. But we observe (after Nathaniel Johnston) that for $n=500$, gliders are produced on the boundaries after $471$ steps, but $471<500$, so this must happens $\forall n \ge 500$.
It follows that the answer is yes.

Improved question: Is the stationary component non-vanishing for any $n > 1000$ ?

Stronger question: Is $p_n \ge 2$ for any $n > 1000$ ?

If the initial position of Conway's game of life is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Can we prove that such a vanishing is not possible for any $n>100$?

Edit: The sequence A061342 gives the period $p_n$ of the stationary component of the final pattern for an initial line of length $n$. But for $n \in [84,1000]$ we have $p_n \ge 2$, so the pattern must be non-vanishing in this case. But we observe (after Nathaniel Johnston) that for $n=500$, perpetual gliders are produced on the boundaries after $435$ steps, but $435<500$, so this must happens $\forall n \ge 500$.
It follows that the answer is yes.

Improved question: Is the stationary component non-vanishing for any $n > 1000$ ?

Stronger question: Is $p_n \ge 2$ for any $n > 1000$ ?

If the initial position of Conway's game of life is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Can we prove that such a vanishing is no more possible for $n>24$?

If the initial position of Conway's game of life is a line of $n \le 100$ cells, then it vanishes completely after some steps iff $n \in \{0,1,2,6,14,15,18,19,23,24 \}$. See below for $n=24$.

Question: Can we prove that such a vanishing is not possible for any $n>100$?

Edit: The sequence A061342 gives the period $p_n$ of the stationary component of the final pattern for an initial line of length $n$. But for $n \in [84,1000]$ we have $p_n \ge 2$, so the pattern must be non-vanishing in this case. But we observe (after Nathaniel Johnston) that for $n=500$, gliders are produced on the boundaries after $471$ steps, but $471<500$, so this must happens $\forall n \ge 500$.
It follows that the answer is yes.

Improved question: Is the stationary component non-vanishing for any $n > 1000$ ?

Stronger question: Is $p_n \ge 2$ for any $n > 1000$ ?