> I would say "the data type of individual tensor elements".
> (so that people don't try to make it e.g. List(float64)).


Also, I don't think any reference to pyarrow should be made here.


Good catch! I have updated the text with:

  * **value_type** is the data type of individual tensor elements
    and is an instance of Arrow ``DataType`` or ``Field``.

I would say the "the physical shape" to make it clear it refers to how
> values are laid out in memory, while `dim_names` and `permutation` drive
> the logical interpretation.


Have updated the description of the shape and added logical layout to the
optional
parameters text::

* Extension type parameters:


  * **value_type** = Arrow DataType or Field of the tensor elements.
  * **shape** = the physical shape of the contained tensors
    as an array.


  Optional parameters describing the logical layout:


Perhaps explain in this example that the logical shape is [500, 100, 200]?
> (if I understand `permutation` correctly)


Updated the text with:

  - Example of permuted 3-dimensional tensor:


    ``{ "shape": [100, 200, 500], "permutation": [2, 0, 1]}``


    This is the physical layout shape and the the shape of the logical

    layout would in this case be ``[500, 100, 200]``.


+1! I put together a quick R implementation as well to see how the
> permutation field fits with our native column-major storage [1]. It worked
> great! Thank you for all of your work assembling all of our collective
> opinions on this :-)
>

That is great to hear! Thank you so much for your input Dewey, it helped to
understand
the R side of things much better.

The updated version of the specification can be found here:
https://github.com/apache/arrow/pull/33925/files

All well,
Alenka

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