Manuscript X-Enter-ST@1 · X-Enter-ST.tex · proposition · f76acc1f
Proposition: Exact scope of supported attachment
Stage A: the inherited host and the frozen coefficient › Support attachment versus laboratory acquisition · lines 416–448 · proof included or linked
X-Enter-ST@1#prop:attachment
The following statements are distinct:
the scalar input contract is used in an experiment whose finite ports lie in the retained regular laboratory;
the continuum coefficient has a certified laboratory-supported realization;
an apparatus acquires that coefficient from unknown continuum field data.
The construction below establishes (i). It preserves (ii) whenever its separate support certificate is supplied, and constructs no map proving (iii).
Proof. A supplied number or status certificate can be installed as finite task data at a regular port without evaluating its continuum definition there. This gives (i).
If the source-specific dependence reserve lies in the chart, the compact density pairing is transported by change of variables, with its density Jacobian retained. That transport preserves its numerical value, giving the conditional assertion in (ii). It does not replace by a cone operator.
Neither a change of variables nor a supplied finite table defines a field-to-apparatus acquisition map. Thus neither argument supplies (iii).