A.19:5.1.1 - Type signature

Each slot i names one U.Characteristic and one chosen Scale:

slot_i = (Characteristic_i, Scale_i).

The Characteristic supplies its subject/input signature: the entity kinds and roles required when it is assigned a value. For a relation Characteristic the signature also gives the role order, or states that the relation is symmetric. A use of the slot binds that participant tuple separately. The tuple is not the Coordinate; the Coordinate is a value on the chosen Scale. C.16 uses the same separation between measurand or subject tuple and measured Coordinate.

The CharacteristicSpace is the Cartesian product of the slots’ genuine Scale value sets:

CS = product_i ValueSet(Scale_i).

A point x in CS supplies one Coordinate x(i) from ValueSet(Scale_i) for every slot. Using that point for a subject separately binds a conforming subject/input tuple b_i and states or evaluates the characteristic assignment between b_i and x(i). For example, the distance Characteristic may bind (Machine-A, Machine-B) while its Coordinate is 3.5 m.

A complete state is total over the selected basis. An observation or evaluation input may instead be partial: it supplies Coordinates only for a subset of slots and records missing, censored, unknown, or another observation status separately. A consumer applies its own applicability and tri-state or error rule before treating such input as a state. not-applicable is normally an applicability fact, not a Scale value; a domain may use it as a genuine value only when the Scale explicitly defines that meaning.

Any U.Dynamics.stateSpace refers to a declared CharacteristicSpace. The dynamics model states the constraints selecting its admitted states within that product, and its trajectories use points satisfying the applicable state constraints. A.3.3.CC constructs the configuration description; A.3.3 supplies additional state information, the dynamic law, time base, observation relation and prediction-use conditions.