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The first of the atariki pair in K maybe is not at Betelgeuze but at Rigel:

*Ka1-17 (13) *Ka1-18 (14) *Ka1-20 (15)
Ga1-13 Ga1-14 Ga1-15
λ Eridani (76.7) μ Leporis (77.6), ĸ Leporis (78.0), Rigel (78.1), Capella (78.4)  

In Ga1-13 the glyph type is slightly different, it is not an atariki (Shadow King) glyph but an ariki (King) glyph. And the constellation is not Orion but Eridanus, close but not the same.

The left foot (rigel) of Orion is in the Eridanus River and his right arm is in the Milky Way. A straight line drawn from the left foot to the right shoulder leads across the Belt of Orion.

From this picture we can guess why there is an incomplete atariki at Rigel. It is similar to Betelgeuze. Down in the waters of a river visability is not good, even worse if it should be a milky river.

The pair of atariki glyphs in K is a 'proof' how the text should be read and also a 'proof' that the stars in the text of K are in parallel with those in the text of G. Their star maps are in parallel. The curve illustrating poor visability in Ka1-17 coincides with λ Eridani.