To A.Plotkin re your translation pages:
You query why the four segments describing the '5' (exponent) function contain
no 'P' (identity) symbols.  For instance, the phrase you render as:

G QCQ5A5 QBQ 5A5QCQ G

If I read your comment correctly, you wonder why this is not given as:

G QCQ5A5 P QBQ P 5A5QCQ G

I think the answer is that the '5'-delimited exponential factor is read as an
operator, rather than part of the number.  The break is thus:

G QCQ 5A5 QBQ 5A5 QCQ G,

or more generally, /a/ 5/b/5 /c/ 5/b/5 /a/ :: c = a^b

For analogy, look to TC 'h' and 'k', the cosine and sine predicates.  I think
'5-5' is an exponent predicate along the same lines.

This is, perhaps, trivial; but I think it provides a sufficient answer so you
won't think the TCs are leaving great gaps in their message.

Regarding the inadequacy of the semicircle imagery noted in your comments,
specifically with regard to left-right or clockwise/counterclockwise
orientation over a serial link:  Could this apparent error on the TCs' part be
a result of their devotion to symmetry?  Some sort of mental block to the
nuances of directionality?  Of course, they appear to have some sense of 
directionality, but they expend an awful lot of their datastream on
symmetrically formatted phrases.

The "planetary names" question is intriguing.  The use of W ("then") seems odd,
but there should be some good reason.  What is it about the 6 '1y1' strings
that would make them deductions from what has gone before?  By the way, I
think it's a mistake to refer to these as '1y1' and so on.  Keeping in mind
the symmetry issue, we really have:

'xz' = the 3-radius hexagon
'wy' = the single dot
'zy' = (i) the diamond and (ii) the 2-radius hexagon
'1y' = (i) the dot, (ii) the diamond and (iii) the 2-radius hexagon

And then,
'2'  = '1y'(1)   '89' = '1y'(3)   '43' = '1y'(5)
'79' = '1y'(2)   '32' = '1y'(4)   '4y' = '1y'(6)

I don't know if this is helpful or not.  At this hour, I can barely focus on
the letters, let alone figure them out.

Anyway, there's some cool stuff in the fourth message relating to powers of
[10], i.e., powers of 6.  I think.

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