Tight resilience threshold for mixed honest mining policies

Determine the tight resilience threshold for Nakamoto consensus when a fraction of honest mining power performs optimistic mining before validation and the remaining honest mining power extends only fully validated chains, including a matching attack threshold for every interior optimistic-mining fraction $0<p<1$.

Background

The paper derives a sufficient security bound parameterized by the optimistic honest-mining fraction pp. It also develops private-fork attacks under delayed validation and network delay, but these attacks do not generally match the sufficient bound for interior mixtures. The carrier attack used for the all-optimistic case does not directly extend when strict miners continue advancing the valid chain, leaving the exact threshold for mixed policies unresolved.

References

This is a sufficient bound. We do not establish a matching attack threshold for $0<p<1$.

— Security Limits of Mining Before Validation in Nakamoto Consensus  (2609.29222 - Zhou et al., 24 Sep 2026) in Appendix F, subsection “Attack scope and unresolved tightness,” and Conclusion

We leave the tight resilience threshold for mixed policies and the effects of validation queues and processing limits for future work.

— Security Limits of Mining Before Validation in Nakamoto Consensus  (2609.29222 - Zhou et al., 24 Sep 2026) in Conclusion