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Weak vanishing of a horizontal line in Conway's Life

TheoremDB P2918 · cellular automata

Inferred from the community field; finer classification has not been reviewed.

Source catalogue assessmentAs of 2026-09-08Source & evidence ↓

Problem statement

In Conway's Game of Life on Z2\mathbb Z^2, start with exactly Ln={(0,0),(1,0),…,(n−1,0)}L_n=\{(0,0),(1,0),\ldots,(n-1,0)\} alive. Does there exist an integer n≥25n\ge25 such that every fixed cell is dead at all sufficiently large times?

Lean 4

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Background

Additional formulation recorded by the source

Decide whether (∃n≥25)(∀x∈Z2)(∃Tx)(∀t≥Tx) x is dead in Ft(Ln)(\exists n\ge25)(\forall x\in\mathbb Z^2)(\exists T_x)(\forall t\ge T_x)\ x\text{ is dead in }F^t(L_n).

Progress & source assessment

Source-reported assessment, retrieved 8 September 2026. Frontier Science has not independently reviewed this status.

Open. No signed Lean verification is attached to this problem or its selected resolution.

References
  1. [1]TheoremDB P2918 link

Recorded progress

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Machine attempts

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Discussion

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