Misunderstanding Recursive Systems And Misrepresenting 'Univariate'

Martin (2013: 70):

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[1] To be clear, this misunderstands a recursive system. The choice in a recursive system is either to go on or stop. Halliday & Matthiessen (2014: 438):

[2] To be clear, these structures are still referred to as univariate, and opposed to multivariate. Halliday & Matthiessen (2014: 390):

We refer to this kind of structure as a univariate structure, one which is generated as an iteration of the same functional relationship (cf. Halliday, 1965, 1979): α is modified by β, which is modified by γ, which is ... . By contrast, the type of structure exemplified by Deictic + Numerative + Epithet + Classifier + Thing we call a multivariate structure: a configuration of elements each having a distinct function with respect to the whole.

[3] To be clear, a complex is a type of univariate structure, one in which rank units are related to one another, as clauses in a clause complex. An example of a univariate structure that is not a unit complex is the logical structure of the verbal group, which is not a complex of rank units. Halliday & Matthiessen (2014: 398-9):

… the elements of the logical structure are not the individual words but certain rather more complex elements. … The logical structure of the verbal group realises the system of tense. … The primary tense is that functioning as Head, shown as α. This is the Deictic tense: past, present or future relative to the speech event. The modifying elements, at β and beyond, are secondary tenses; they express past, present or future relative to the time selected in the previous tense. Realisations are shown in Table 6-12.