The critique is that the current nomenclature does not accurately reflect the concept it intends to describe. For example, under the existing terminology, a set like ${\emptyset, ABC}$ could be labeled a linearization even though it fails to sequentially order the elements A, B, and C. This leads to a proposal for adopting a new term, "escalating grouping," which more precisely captures the essence of the process. In this proposed framework, transactions are grouped such that each group can be ordered hierarchically where every group preceding another is a proper subset, and every group following is a proper superset, starting with the empty set and culminating in the final group.

Further distinction is suggested within this framework between "fully escalating groupings" and "partially escalating groupings," with the possibility of retaining the term linearization for the former while possibly introducing a new term for the latter, humorously suggested as "minilinearisation" due to its smaller scope compared to full linearization. This nuanced approach aims to provide clearer, more descriptive terminology that better aligns with the underlying processes being described.

Additionally, there's a technical critique regarding the function compose, questioning its return value and suggesting a revision to ensure that the element 's' is specified as topologically valid. This point underscores the importance of precision and clarity in mathematical functions and their definitions to avoid ambiguities and inaccuracies in their application or interpretation.