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I will now list the glyphs in line Ka1 with stars and dates, exactly as was done for the G text. The dates could in principle be different from those in G, but I guess they are the same. The structure of a calendar should be the common property of a people.

Ka1-1 Ka1-2 Ka1-3 Ka1-4
  Ain, θ¹ Tauri, θ² Tauri (65.7)   Aldebaran (68.2)
'May 25 '26 '27 '28
Sheratan 9 10 11 12
Ka1-5 Ka1-6
Theemin (68.5)  
'May 29 '30 (150)
Sheratan 13 14

Moonday at Ka1-6 could correspond to the old Pre-Julian calendar's position for the end of the first quarter:

... Perhaps the extra night Sheratan 14 in a way corresponds to an extra day 'May 30 in the Gregorian calendar. Julius Ceasar did not add any day to Maius, it already was 31 days long. But the old Roman calendar reached night 91 (= 31 + 29 + 31) with Maius 31. Therefore the extra night Sheratan 14 could correspond to the 'corner' beyond 360 / 4 = 90 ...

The vero sign probably indicates the final of the rainy quarter. In front the crescent 'ear' could refer to the Pleione manzil beginning next day.

Ka1-7 Ka1-8 Ka1-9 Ka1-10
      Hassaleh (73.6)
'May 31 'June 1 '2 '3
Pleione 1 (15) 2 3 4
-
Ka1-11 Ka1-12
Almaaz (74.7), Haedus I (74.8) Haedus II (75.9), ε Leporis (76.0), Cursa (76.4)
'June 4 '5h (76.1)
Pleione 5 6 (20)
-
*Ka1-17 (13) *Ka1-18 (14)
λ Eridani (76.7) μ Leporis (77.6), ĸ Leporis (78.0), Rigel (78.1), Capella (78.4)
'June 6 (157) '7
Pleione 7 8 (22)
*Ka1-20 (15) *Ka1-21 (16) *Ka1-22 (17) *Ka1-23 (18) *Ka1-24 (19)
  λ Leporis (79.6) Bellatrix, Saif al Jabbar (80.7), Elnath (80.9) Nihal (81.7), Mintaka (82.4)  ε Columbae (82.6), Arneb (83.0), Heka (83.2)
'June 8 '9 '10 '11 '12 (163)
Pleione 9 10 11 12 13 (27)

My colours fit with the Gregorian dates if we count the visible glyphs only. The jump from Ka1-12 across a vacant space to the next glyph could have to do with the fact that the first 5 right ascension hours are over.

The first glyph line in K (and also the manzil Pleione) ends with Heka (the head of Orion, the Chinese Turtle Head):

20 Turtle Head Heka (83.2) *Ka1-24 (19) 'June 12 (163) Pleione 13 (27)
Ga1-19 (20)
21 Three Stars Alnitak      
22 Well Tejat Posterior