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Long-term fate of co-evolution under mixed deterministic–stochastic regimes

Determine whether, in the bitw0r1d framework under regimes where one process (either the technological system T or the search space S) adopts changes deterministically while the other adopts changes stochastically, the co-evolution of T and S persists indefinitely or eventually reaches an absorbing barrier for a given simulation run.

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Background

The authors report that when one of the two co-evolving processes is strongly deterministic and the other strongly stochastic, some runs reach the maximum generations. However, due to stochasticity, they cannot conclude whether such dynamics will inevitably continue indefinitely or terminate at an absorbing barrier in any specific run.

References

Simulation runs in these instances are capable of reaching 10, 000 generations, but stochastic nature of the dynamics means we cannot definitively state for a given simulation run whether T and S will keep co-evolving indefinitely or eventually hit an absorbing barrier (see Figure 1).

— Modelling the emergence of open-ended technological evolution (2508.04828 - Winters et al., 6 Aug 2025) in Section 3. Results (Figure 3 context)