Relate semi-causality to other causality notions

Prove or refute the conjectured implications and equivalences relating strong semi-causality, absolute microcausality, and Einstein and weak microcausality for localizable groupoid quantum reference frames with identity-centered localizing sequences.

Background

The paper introduces strong and weak semi-causality in addition to absolute, strong, and weak microcausality and ordinary relational causality. It explicitly conjectures stronger relationships among these conditions under localizability and the existence of suitable localizing sequences, but does not prove them.

References

We conjecture that if R is localizable and there exists localizing sequences centred around the identity in SR, then strong semi causality implies absolute microcausality, and Einstein causality becomes equivalent to weak microcausality. We keep such considerations for future work.

— A groupoidal approach to quantum reference frames  (2608.14133 - Fedida et al., 14 Aug 2026) in Remark 6.26, Section 6.3, p. 51

Following up on Rem. \ref{Rem:reldynamics}.\ref{itm:Rem:reldynamics1}, it is a general theoretical question for models based on (relativistic) quantum dynamics, whether there exist examples in which strong locality is violated yet weak locality is not .

— On the applicability of Kolmogorov's theory of probability to the description of quantum phenomena. Part II: Bell inequalities  (2609.31075 - Reddiger, 25 Sep 2026) in Section 7, Conclusion and outlook, final paragraph of the future-work discussion