A species-bundle convention with its parameter exposed

Definition def:Eres is a genuine definition of a family. For each parameter it identifies the total space, projection, dual test space, and scalar pairing. It does not choose the parameter which the frozen joint-map target uses. This is the strongest codomain completion justified without silently inserting an output fiber convention.

One could choose an explicit tensor-product value bundle for the mixed residual slots and compute its rank. That would be a legitimate additional mathematical convention. It would also have to specify the covariant or contravariant value convention, its density, and its identification with the target's contraction indices. This patch does not make that extra choice under the label “from XIV-G.”

The reason for leaving the parameter visible is not that a printed integer is intrinsically necessary for defining a distribution space. A vector bundle defined by explicit bundle operations is an object even if its rank is not separately printed. The missing point here is the identification of the actual output fiber and pairing, not the typography of a dimension statement.