Minimize the record count of a self-reproducing stored network

Determine how few records a self-reproducing stored network can use while retaining the paper's exact self-reproduction mechanism and the associated stored-network construction requirements.

Background

The paper gives explicit self-reproducing stored networks, including a 143-record organism and a stored SUBLEQ host with 36,080 records for the eight-bit instance. These constructions demonstrate existence but do not optimize the number of records. The conclusion explicitly leaves open the minimization problem: identifying the smallest record count achievable by any self-reproducing stored network under the framework considered.

References

Other questions are open: whether a ternary step of SUBLEQ can have depth below $11$, since Lemma~\ref{lem:muxdepth} and Remark~\ref{rem:ternarydepth} bound only a read and the branch; how few records a self-reproducing stored network needs; and how much noise a reproducing run tolerates when the perturbations are correlated or drift, which the independence assumed in Section~\ref{sec:robust} excludes.

— Universal Construction and Exact Self-Reproduction in Ternary McCulloch-Pitts Networks  (2610.12251 - Norton, 8 Oct 2026) in Section 9, Conclusion (following the discussion of the fixed network's non-reproduction)