Gottschalk's surjunctivity conjecture
Gottschalk's surjunctivity conjecture* (1973): every group is surjunctive. That is, for every group G and every finite alphabet A, every injective cellular automaton on A^G is surjective.
Mathematical statement
Gottschalk's surjunctivity conjecture* (1973): every group is surjunctive.
That is, for every group G and every finite alphabet A, every injective cellular
automaton on A^G is surjective.
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Statement artifacts, not proofs
These records expose exact Lean propositions and statement-only wrappers. Defining a proposition does not supply a proof of it. A placeholder-bearing target also contains no proof. Elaboration checks syntax and types; it does not certify that a formalization perfectly captures every nuance of the informal problem.
Pinned Lean formulation 1
gottschalk_surjunctivity_conjecture
theorem gottschalk_surjunctivity_conjecture (G : Type) [Group G] : IsSurjunctive G := by sorry- Statement source
- Formal Conjectures
- Lean version
- v4.27.0
- Placeholder
- Present; no proof artifact
- Source evidence
- Pinned source index
- Fidelity review
- Community formulation
References