Operating under a genealogical metric of veridiction, a pathway functions to orient inquiry. It picks out and connects elements in a heterogeneous and dynamic contemporary problem space. It consists of parameters whose function is focus attention on problems, indeterminacy, discordancy, events (episodes) and ramifications. Unlike a recursive series of categories in a diagnostic whose logic and form is analytic, a pathway genealogically reduces historical complexity to a path-connected set of nodes.

One way of approaching inquiry is through multiple graphings of topological pathways organized so as to elucidate problems.

In mathematics, a path in a topological space X is a continuous map f from the unit interval I = [0,1] to X   f : I → X. The initial point of the path is f(0) and the terminal point is f(1). One often speaks of a "path from x to y" where x and y are the initial and terminal points of the path. Note that a path is not just a subset of X which "looks like" a curve, it also includes a parametrization. For example, the maps f(x) = x and g(x) = x2 represent two different paths from 0 to 1 on the real line. A topological space for which there exists a path connecting any two points is said to be path-connected. Any space may be broken up into a set of path-connected components. The set of path-connected components of a space X is often denoted π0(X);.

a fact or circumstance that restricts how something is done or what can be done; a variable value that, when it changes, gives another different but related mathematical expression from a limited series of such expressions