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Identify more discriminating necessary conditions for universal self-replication

Develop additional, more discriminating necessary conditions—beyond local universality and the local self-replicating condition—that characterize when a cellular automaton can belong to the UniversalSelfReplicating class.

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Background

The authors formalize a minimal local self-replicating condition and prove separations between local universality, universal self-replication, and global universality. They note that while their condition is necessary, stronger criteria are desirable to better differentiate which dynamics support universal replication.

They explicitly state that they currently lack other more discriminating necessary conditions.

References

At the moment, we do not know of any other more discriminating necessary conditions, and we will discuss this later.

— Self-replication and Computational Universality (2510.08342 - Cotler et al., 9 Oct 2025) in Section 'Open problems and conjectures' (Genericity of universality and self-replication)