Coordination Measures for Learner–Agent Dyads under Bandwidth Constraint

A companion position paper has argued that under severe bandwidth constraint the improvement cycle in DeafBlind education must be owned by the learner, because no sighted-hearing party can evaluate the semantic yield of a tactile output. That argument leaves a metrological hole. If quality cannot be specified externally, what is measured, and by what estimator? This paper closes the hole. It takes a published four-component coordination measure developed for multi-agent ensembles — the EDP-Φ Bridge of Kremenchutskiy (2026a) — and asks whether it transfers to a dyad consisting of one learner and one assistive agent. It does not transfer intact. Two of the four components are shown to degenerate at n = 2: the revision-capacity term, defined as the second-smallest eigenvalue of an agreement-graph Laplacian, reduces to a single edge weight and carries no structural information; and the coherence term, defined as a variance across ensemble members, is not an ensemble statistic when there are two members. Both are replaced with within-dyad, longitudinal substitutes that preserve the intended construct while surviving the degeneracy. The result is a four-measure instrument with named estimators and, for each, a stated falsifying observation. The instrument is offered for evaluation by DeafBlind researchers and practitioners; the authors do not claim it has been validated, and §7 states what would be required to validate it.