Hi Terrence, 
Firstly, I admire your energy trying to come to grips with these
concepts. I find myself glossing over most of this "theory" and just
trying to get things to "work". However, but I realise that I'm going to
have to come back to it at some stage if I want to achieve the next
level of proficiency in the language.

So given that background, my interpretation below may not be entirely
correct, but here goes anyway.

> x,y appends items of y to items of x after:
> 
>   1.  Reshaping an atomic argument to the shape of the items of the
>       other,
> 
> The items of i. 2 3 are of shape 3. So 7 becomes 3 $ 7 or 7 7 7
> 
> 
>   2.  Bringing the arguments to a common rank (of at least 1) by
>       repeatedly itemizing (,:) any of lower rank, and 
> 
> I cant figure out what expression is being used on 7 7 7 
> here... help needed 
>

7 7 7 now has the same shape as the items of i. 2 3 so can be appended
to the the items of x

 
>   3.  Bringing them to a common shape by padding with fill elements
>       in the manner described in Section II B. 
> 
> Not entirely sure about this either.
> 

Don't think this required for your example as 7 7 7 aready has common
shape with the items of x.

If the expression had been (i.2 3) , ,7
Then the right noun rank would already be 1 and so after step 2. it
would still be (,7). To bring them to common shape it would then be
padded with zeros (7 is numeric).
   (i. 2 3) ,,7
0 1 2
3 4 5
7 0 0   
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