Operational Articulation Horizons: Residual Indistinguishability, Structural Plurality, and Dual Monotonicity

Operational reconstruction can fail in two mathematically distinct ways. First, different internal objects may remain indistinguishable within a fixed articulation; this is a vertical or residual horizon. Second, the same operational presentation may support several inequivalent articulations, even when it is globally informationally complete; this is a horizontal or structural horizon. This note separates these two axes through an articulation-horizon spectrum and distinguishes class uniqueness, invariant class selection, and invariant representative selection. For exact finite-dimensional quantum presentations, every factor witness with joint algebra isomorphic to a full matrix algebra has a residual multiplicity determined by its commutant. The restriction of states to the accessible algebra is injective exactly when this multiplicity equals one. Under operational enrichment, observation fibers and commutants shrink, while the raw set of subset-generated structural witnesses can expand. The resulting articulation-horizon spectrum is equivariant under global unitary changes of presentation. An explicit three-qubit construction is exhaustively enumerated. The enriched presentation contains exactly seven direction-generated embedded qubit-factor algebras and exactly three inequivalent finest full tensor frames. Operational completion reduces the residual multiplicity from two to one while revealing complete structural plurality rather than a unique subsystem decomposition. The results remain entirely at the operational articulation layer and do not identify an exposed factorization with an exhaustive ontological partition.