Consistency of the periodic dual-number stationarity hypothesis in constructible set theory

Establish whether the periodic dual-number stationarity hypothesis PDS is consistent relative to ZFC, specifically whether Con(ZFC) implies Con(ZFC + (V=L) + PDS).

Background

The paper introduces PDS as an auxiliary hypothesis used to derive the universal equality GP(A) = PGF(A) for every ring A under V=L. It explicitly states that the consistency of PDS relative to ZFC is unknown and formulates the stronger relative-consistency assertion that PDS is compatible with ZFC together with the axiom of constructibility.

References

We do not know whether $\textsf{ZFC}+\textsf{PDS}$ is consistent relative to $\textsf{ZFC}$, and we do not know any familiar set-theoretic axiom or hypothesis that implies $\textsf{PDS}$. Thus we make no consistency assertion for $\textsf{ZFC}+\textsf{(V=L)}+\textsf{PDS}$; the result is only a conditional implication.

— A strongly compact cardinal yields a left and right coherent ring with $\mathcal{PGF}(R)\subsetneq\mathcal{GP}(R)$  (2608.17748 - Zhang, 18 Aug 2026) in Section 4, Discussion of related consistency questions, Conjecture \ref{conj:pds-in-L}