Parametric Realizations of Coherence Evaluation in Minimal Systems

This technical note develops minimal parametric realizations of coherence evaluation in explicitly modeled systems. It shows that a geometrically defined notion of coherence can be rendered computationally explicit once three elements are specified: a state space, an admissible domain, and a metric. A general parametric template is introduced in which coherence is defined as the distance from the current state to a domain of structurally compatible states. Several classes of admissible domains are distinguished, including interval, polyhedral, and smooth constraint-defined cases, and low-dimensional examples are provided. A weighted metric extension is also considered to accommodate unequal regulatory significance across state-space dimensions. The note does not introduce a new architectural layer of the broader framework. It serves a supplementary role by clarifying the formal realizability of coherence evaluation while distinguishing this question from issues of internal representation, empirical reconstruction, and dynamic transformation of admissible domains.