Fiber product diagrams in the olog.**

**Some boxes in the olog (Figure 4) are defined in terms of others by use of so-called fiber products. For example, object A is defined in terms of three others in relationship, D→H←G: given a system of bricks, glue, and lifeline (D), we observe its structure graph (H) and set it equal to a “chain graph” (G) – in so doing we define “one-dimensionality” for a system. A reader of this olog realizes that our notion of one-dimensionality is not up for interpretation, but directly dependent on the other notions in this olog. By having this additional data, we confine the meaning of 24 labels (8 for boxes, 16 for arrows) in the olog. Thus this table serves to anchor the interpretation of our olog more firmly to its original intention. [For a more diagrammatic description of the same information presented in the typical style of category theory, see Figure S2.].