Coherence Field Equation (CFE): A Technical Note on a Proposed Field Formalism for Conversational Coherence

This technical note introduces the Coherence Field Equation (CFE), a proposed field-based formalism for modelling conversational coherence as a dynamic, distributed process rather than a static or binary property. The note is written as a research scaffold, not as a validated theory. Its aim is to provide a formal vocabulary for representing coherence in terms of propagation, degradation, reinforcement, and interaction with boundaries or constraints across a conversational trajectory. The document extends Hykon’s broader runtime-governance framing by proposing: a scalar coherence field, a directional flow term, a proposed continuity-style relation linking local change to coherence flux, and a provisional rotational component intended to model orbit-like or recirculating conversational behavior near unresolved attractors or boundary conditions. It also includes a simple cosine-similarity proxy as a low-order practical approximation, while explicitly noting that such a proxy does not validate the full formalism. This work should be read as a technical note and modelling proposal. It is intended to support critique, testing, refinement, and possible downstream operationalisation within interaction-layer governance research for conversational AI. The note is explicit about its current limits: the formalism is not empirically validated, is not claimed to be uniquely correct, and includes provisional components that remain open to revision or removal. Keywords: conversational coherence, runtime governance, inference-time control, language models, formal modelling, field formalism, trajectory dynamics, Hykon S-OS