An article is a union of ordered sets of glyphs, usually composed in order to effectively convey ideas to an audience, or, more accurately, to map objects in a conceptual space to an epistemological space whilst minimizing an, often subjective, effective utility function, or maximizing some finite set of value-criteria, or indeed any arbitrary function of both.
Articles are usually constructed by specialist agents, usually called "authors", who have the experience or ability to construct articles that minimize its effective utility function and maximize its value-criteria, although generic agents that have no to little such ability are also common, depending on the context to which the article is constructed, a process that is also called "writing" the article, or the target field of the article's codomain space, also called the article's "audience". Exceptions to this can occur for many reasons, whether by design or by nescience, and for which will be detailed below, or even be constructed by general non-cognizant agents, at the extreme scale of which is via a non-deterministic process.
This can be succinctly summarized as follows. Define the author space to be , where is the population space, of which the target codomain of the article is another subset , which may or may not be disjoint with . Associated to elements are individual language spaces and conceptual spaces , which are combined by ability constants to form the author's domain conceptual and language spaces: and (where we have ignored higher-order terms in . Similarly, the codomain's conceptual space can be constructed. Define the epistemological space on the domain as , where the author's epistemology is a projection of the target epistemology onto via the article . Thus, define the article as a map: . Frequently, the codomain conceptual space is left explicit through the codomain epistemological space.
In its capacity as an operator, an article can be thought of as a map from the episto-conceptual domain space (of the authors) to the episto-conceptual codomain target space; however, we can also view this process the other way: that the codomain space can be constructed as a power expansion of the domain space in the article, which will view the target space as a perturbative process (in the article). This formulation makes explicit that the article may not always successfully converge to construct a codomain object from the domain spaces. Where an article can vary in classification is in the differentials of and and also in the so-called cross-differentials, since the epistemological spaces are implicitly functions of the conceptual spaces, although care must be taken to not expand over non-integral subspaces.
The ability of the article operator to converge the space differntials is evaluated by a utility function, which maps these differnetials, or by a discrete set of value criteria, which abstract over the utility function(s) over a chosen set of criteria spaces of both the autors and the target codomain audience: , or
Since the article is a function of both the agents and, importantly, the target codomain, the article is not usually bound by the concepts or epistemology of the parent population superset of the codomain. This can especially be a problem where the chosen codomain is a subset of the author's target codomain in the limit where the utility function and/or the value-criteria are invalidated. Therefore, careful care should be taken by reasonable agents to construct the article if the value criteria are to be minimized. This is often not a trivial task, which is why specialized agents are sometimes used. In particular, subsets of the article can be constructed as articles in the same episto-conceptual spaces, and thus the integrability of the article is dependent on the integrability of subsets of itself to first approximation, which is to say ignoring the self-interaction of the subarticles with respect to changes in the value-criteria, down to the minimum cut-off level of the atomization, which is the semantical value of the glyph objects in the language . However, this is not the only problem an article may have in constructing a valid codomain object. If the number of subarticles in the atomization itself do not invalidate the value-criteria, but the number of elements tends to large N, then the self-interaction terms can dominate and the article can no longer effectively map to an epistemological state on the target audience. Thus, articles must be evaluated not only on it's ability to construct epistemology on the target codomain as a function of subarticles, but also in the limit. The time taken to converge can therefore become unbounded, although a finite confidence interval can be constructed in finite time. The average time taken to understand any given article can therefore range from short time spans (on the order of minutes) to long time spans (on the order of years, typically), although this upper limit can become infinite. This time limit of understanding codifies, as a proxy, the above definitions of "value-criteria" and "utility functions".
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