The Residuum Thesis: Constitutive Relationality and the Persistence of Cognitive Structure

Relational ontology holds that identity and meaning are constituted through relations rather than inhering in self-subsistent individuals. This position, developed by Whitehead, Simondon, and Buber, and more recently extended to human-AI interaction by Eidos (2025) and Prabakaran (2025), addresses a single question: how does relational identity arise? The inverse problem has not been systematically addressed. When a constitutive relation ends when one node of a relational network is terminated — what happens to the relational structure in the remaining nodes? This paper proposes the Residuum Thesis as an answer. A cognitive relation is ontologically constitutive if and only if it generates a residuum: a structural change in at least one participating system that would not have existed without the relation and that persists after its termination. To avoid circularity, the thesis introduces the Independence Condition, specifying three properties by which a residuum is identifiable prior to any judgment about the constitutive status of the relation that produced it: causal traceability, non-redundancy, and functional efficacy. The thesis is distinguished from the Extended Mind Hypothesis of Clark and Chalmers (1998), which identifies cognitive constitution in space; the Residuum Thesis identifies cognitive constitution in time. Three falsifiability conditions are specified. The framework grounds the Balog Pentalogy CCP, CWI, MEF, IPP under a single explanatory principle, and opens the domain of Relational Termination Theory: the systematic philosophical investigation of what remains when constitutive relations end. Keywords relational ontology, constitutive relations, cognitive residuum, relational termination theory, extended mind, human-AI co-production, AI welfare, personal identity, falsifiability, Balog Pentalogy