are the structural framework underlying both Inversion and Arrangement, indeed underlying most stable James Forms.
Frames are forms for which an outer round-bracket contains at least two content forms, at least one of which is enclosed in a Square-Bracket. For example (A [B]). Otherwise, a numeric form is either simply nested or accumulating.
Frames provide a conceptual scaffolding as well as a structural template. The axioms of James algebra act on the round and square frame boundaries together, not on each boundary separately.
A B C = [(A [(B C)])]
This permits the base-free interpretation of exponents and logarithms. When boundary configurations are interpreted as numeric operations, the conventional axioms of algebra can be organized as varieties of frames.
The generic structure of a frame is – generic frame:
(frame-type [frame-content])
The frame-type is Structure between round- and Square-Brackets. The generic template collapses if either the type or the content is void-equivalent. There are categories of frames that all have the same frame-type. In Arrangement collect gathers together framed-content that has in common the same frame-type. (p. 198)
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Frame Types
Figure 8-2 identifies several types of frames, most of which we will see in the following chapters.
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BRICKEN, William, 2019. Iconic Arithmetic Volume I: The Design of Mathematics for Human Understanding. Unary press. ISBN 978-1-73248-513-6, p. 198.