A criticism of Cramer's 2015 account of dealing with multi-particle quantum systems is found in Kastner 2016, "An Overview of the Transactional Interpretation and its Evolution into the 21st Century, Philosophy Compass (2016). It observes in particular that the account in Cramer 2015 is necessarily anti-realist about the multi-particle states: if they are only part of a 'map,' then they are not real, and in this form TI becomes an instrumentalist interpretation, contrary to its original spirit. Thus the so-called "retreat" to Hilbert space (criticized also below in the lengthy discussion of note) can instead be seen as a needed expansion of the ontology, rather than a retreat to anti-realism/instrumentalism about the multi-particle states. The vague statement (under) that "Offer waves are somewhat ephemeral three-dimensional space objects" indicates the lack of clear definition of the ontology when one attempts to keep everything in 3+1 spacetime.