> ... the presence of a **`dimensions`** attribute on  a scalar variable will 
> identify the
variable as a domain variable.

There is some confusion here ... Are we saying that a domain variable _must_ be 
a scalar? We don't insist on that for grid mapping and geometry variables 
(although it is [recommended for grid mapping 
variables](https://github.com/cf-convention/cf-conventions/blob/master/conformance.adoc)).
 If we say that for a domain variable, we should say the same for grid mapping 
and geometry variables - which I think would be a defect change (on the grounds 
that these variables were never intended to contain meaningful data arrays).

Either way, this brings me back to @JonathanGregory's suggestion of disallowing 
`dimensions` as a data variable attribute, which I now think is OK (for CF 
versions starting at the one in which the domain variable goes in). So that 
first sentence could become

```
The dimensions of the domain must be stored with the **`dimensions`**
attribute, and the presence of a **`dimensions`** attribute identifies the
variable as a domain variable. Therefore the *`dimensions`** attribute must
not be present on any variables that are to be interpreted as data variables.
```
The phrase *variables that are to be interpreted as data variables* means that 
variables that are *referenced* by data variables (such as auxiliary coordinate 
variables) may indeed have a **`dimensions`** attribute, but in that case such 
a variable cannot also be used as independent data variable (see, for example, 
the section "Interpreting CF-netCDF files" in 
https://doi.org/10.5194/gmd-10-4619-2017).

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