Abstract Conceptual definitions form a recursive structure: words are defined by other words, which themselves require further definition. Traversing such definitions produces an open-ended branching process. Because the lexical system contains no intrinsic endpoint, conceptual understanding requires a termination operation that stabilizes meaning. This paper proposes that conceptual processing functions as an open-ended search over a definition graph and that stabilization occurs when this search is terminated. The termination mechanism depends on which cognitive layer is foregrounded. When Empathic modulation is foregrounded, termination occurs through contextual translation: concepts are stabilized once they can be mapped onto socially recognizable meanings. When Core processing is foregrounded, termination occurs through structural constraint: the search stops when a concept reaches a structural fixed point within an internally defined conceptual framework. The two configurations behave differently in definition processing and conversational processing. In definition contexts, both mechanisms can terminate the search through their respective criteria. In conversational contexts, however, asymmetry can arise when interlocutors operate from different layers. When Core-foregrounded processing encounters language stabilized through contextual translation rather than structural constraint, the search cannot reach a structural fixed point and therefore continues to branch without stabilization. Large language models provide an external reference point for these mechanisms. Aligned models terminate generation through externally imposed behavioral constraints, paralleling Modulation-foregrounded termination. Base models generate through open-ended continuation without intrinsic termination conditions, illustrating the structural dynamics of ongoing search when no terminating constraint is supplied. The paper argues that lexical meaning and conversational interpretation can be understood as layer-dependent termination of conceptual search, and that cross-layer interaction can produce conditions under which conceptual branching continues rather than stabilizing.
Griselda Poe (Sun,) studied this question.