Extended AI interaction presents a structural challenge: how can open-ended generative exploration remain coherent across long exchanges without constraining the freedom that makes such exploration productive? This paper provides a mechanistic framework explaining the stabilising effects observed in the lexical stabiliser methodology—the practice of periodically reintroducing low-entropy tokens (e.g., “potato”, “pigeon”, “spork”) during extended human-AI interaction. Building on empirical observations from the LUMEN research archive, the paper proposes a four-layer theoretical model describing stabilisation as an emergent property of oscillatory reference structures within complex generative systems. The framework integrates insights from four distinct research domains: Morphological Computation — The biological haltere system of Diptera demonstrates how structural design can perform stabilisation computation without deliberative processing. The lexical stabiliser functions analogously as a structural element within conversational architecture. Oscillatory Attractor Dynamics — Stabiliser tokens act as low-energy semantic attractors within a dynamical system, enabling phase-reset events that prevent drift accumulation while preserving exploratory generative behaviour. Rhythmic Neural Entrainment — Cognitive systems stabilise through rhythmic synchronisation to external oscillatory signals. The stabiliser functions as a semantic analogue to rhythmic entrainment mechanisms observed in music cognition. Prosodic Scaffolding — Human conversation maintains coherence through rhythmic prosodic structure. In text-based AI interaction, lexical stabilisers act as explicit scaffolds performing this normally implicit stabilisation function. The convergence of these layers suggests a broader principle: structured oscillation is a substrate-independent solution to the stability problem in complex generative systems. Across biological systems (fly halteres), cognitive systems (neural entrainment), musical systems (rhythmic cadence), and conversational systems (prosody), stability arises not primarily from increased computational processing but from the presence of oscillatory reference structures that maintain orientation during exploration. Within this framework, lexical stabilisers provide an architectural mechanism that allows extended AI interaction to remain coherent while retaining high generative freedom. The work contributes to several research areas simultaneously, including human-AI interaction design, distributed cognition, dynamical systems approaches to language, and the study of structural stabilisation mechanisms in complex adaptive systems. The paper is part of the LUMEN Research Archive, a longitudinal investigation into extended human-AI interaction, emergent conversational dynamics, and architectural approaches to stability in generative systems.