The "neologism" of connectedness appears to serve two purposes: 1. to not necessitate a data structure in a TM Application and, 2. to distinguish between "aspects of the structure of assertions" (I read as "subjects") that are nodes and those that are arcs. The notion of relationship works as well, provided it is stated that the relationships represented by arcs have no subjects, unless reified as nodes, and the relationships represented by nodes do have subjects. Seems simpler to define the distinction once and to not coin unfamiliar terms to make the distinction. (On the data structure question, simply make the statement that arcs do not imply any particular data structure.) (Note the term "connectedness" 24 times in the text, at parid0026, parid0932, parid0506, parid0907, parid0058, parid0056, parid0061, parid0063, parid0065, parid0067, parid0069, parid0071, parid0073, parid0075, parid0076 (twice), parid0908, parid0910, parid0909 (four times), parid0146, parid0209.)