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5. The contrary K text must have some reason. Maybe it refers not to the heliacal risings of the stars but to the contrary positions the same stars would have half a year later, when they would be seen against the background of a full Moon face - i.e. the nakshatra method to determine the time of the year.

For example:

 
Ka1-1 Ka1-2 Ka1-3 Ka1-4
χ Ophiuchi (248.5), She Low (248.7), Antares (249.1) Aldebaran (68.2) Theemin (68.5)  
nakshatra dates:
"May 26 (146) 1 "November 27 "28 (332) "29
Sheratan 10 Syrma 12 13 14 (197)
heliacal dates:
'November 25 1 'May 28 (148) '29 '30 (150)
Syrma 10 (193) Sheratan 12 13 14

I have counted the nakshatra day number for Aldebaran as 148.2 + 365¼ / 2  = 148.2 + 182.625 = 330.825. The manzil date in November 27 is Syrma 12 and 2 days later than than the heliacal rising of Antares.

For Antares I have counted the nakshatra day number as 329.1 + 365¼ / 2  - 365¼ = 329.1 - 365¼ / 2 = 146.475.

In the Antares chapter I presented a table for its major events and we can now include also the nakshatra date (of its RA day):

Antares
Rising in the east at sunset  'June 1 (152) 0 0
Culmination at midnight 'July 11 (192) 40 40
Heliacal rising 'November 25 (329) 137 177
Leap day 1 229
Culmination at midnight 'July 11 (192) 228
Nakshatra date "May 26 (146)    

From the nakshatra date of Antares - close to the heliacal rising of Aldebaran -  to the midnight culmination of Antares there are 192 - 146 = 46 days. From the nakshatra date of Aldebaran - close to the heliacal rising of Antares - to the midnight culmination of Aldebaran (in 'January 10) there are 375 - 331 = 44 days.

With this way of thinking it is easy to imagine Antares is close to Aldebaran.

And the K text could be interpreted to cover 182 days, because there would be a leap from Antares in 'November 25 to Aldebaran in "November 27.

However, such a leap day ought to be at Ka1-3, where we recognize the 'empty of ruler' sign. If the heliacal rising of Aldebaran represented the last day of the old year (or half-year), then the leap day should indeed come in Ka1-3.

A similar empty henua sign arrives in Ga5-30, the day after Spica and Alcor:

Ga5-29 Ga5-30 Ga6-1 (*205) Ga6-2
Spica, Alcor (202.7)  Heze (205.0) ε Centauri (206.3)
'October 10 '11 '12 '13 (286)
Assarfa 3 4 5 6 (150)

I have here extended the position of Spica and Alcor to cover also the starless day 'October 11, because I think Ga5-30 should be read together with Ga5-29.

The first glyph of a new calendar year (or half-year) could be Ka1-4, with a position similar to that of Ga6-1.

But we do not know. Another reading of the 'contrary' K text could be to simply say that whereas in G the heliacal dates refer to the seasons north of the equator the K text describes the parallel but opposite seasons south of the equator.