Strong universality of the EM43 rule space

Determine whether the four-state, radius-1 EM43 cellular-automaton rule space contains a strongly universal rule and, if so, identify an input-output interface compatible with that rule.

Background

EM43 achieves exact extrapolation on several one-input arithmetic tasks but performs poorly on two-input multiplication. The paper cannot isolate whether this failure arises from limited compute, hyperparameters, interface design, or insufficient automaton expressivity. Although the rule space may contain weakly universal rules, the authors explicitly state that strong universality and a compatible interface are unknown.

References

Although the EM43 rule space likely contains weakly universal rules\footnote{\begingroup9pt\raggedright Given that weak universality already appears in the 2-state, radius-1 case through Rule 110. \par\endgroup}, it remains unknown whether it contains a strongly universal rule and, if so, what interface would be compatible with it.

— Emergent Models: Intelligence from Tiny Substrates  (2608.14019 - Bocchese et al., 14 Aug 2026) in Section 3.1, “EM43,” Results discussion