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5. The 11 new Gemini stars added to the star list are distributed in the K text as follows:

Ka3-1 Ka3-2 Ka3-3 (*108) Ka3-4
Alzirr (105.7), Muliphein (105.8) Wezen (107.1)  θ Gemini (107.6)  
'July 5 (186) '6 '7 '8
Al Tuwaibe' 10 11 12 (52) 13
Ka3-5 (46) Ka3-6 Ka3-7 Ka3-8
Wasat (109.8), Mekbuda (110.5) Aludra, Propus (111.1)  Gomeisa (111.6), ρ Gemini (112.1), τ Gemini (112.3) Castor (113.4)
'July 9 '10 '11 '12 (193)
Heka 1 (54) 2 3 4
Ka3-9 (50) Ka3-10 (*115)
λ Gemini (114.0)  Markab Puppis (114.7), Procyon (114.9)
'July 13 '14 (195)
Heka 5 (58) 6
Ka3-11 (52) Ka3-12 Ka3-13 Ka3-14
σ Gemini (115.7), ι Gemini (116.0), Pollux (116.2) Azmidiske (117.4)   υ Gemini (118.6), ο Gemini (119.4) 
'July 15 '16 '17 '18 (199)
Heka 7 8 9 10 (63)
Ka3-15 (*120) Ka3-16 Ka3-17 Ka3-18 (59) Ka3-19 (*124)
χ Carinae (119.9) Jīxīn (120.7), Naos (121.3) π Gemini (121.5), Heap of Fuel (122.1) φ Gemini (123.0), Tegmine (123.3) Al Tarf (124.3)
'July 19 (200) '20 '8h (121.7) '22 '23 (204)
Heka 11 (64) 12 13 Alhena 1 2 (68)
Ka3-20 Ka3-21 Ka4-1 Ka4-2 (64) Ka4-3
Bright Fire (125.4) χ Gemini (125.6), Avior (126.4)  ο Ursa Majoris (127.4) θ Cancri (128.2), η Cancri (128.5)  
'July 24 '25 '26 '27 (208) '28
Alhena 3 4 (70) 5 6 (72) 7
Ka4-4 (*130) Ka4-5 Ka4-6
π¹ Ursa Majoris, δ Hydrae (129.6), Al Minhar al Shujā, Museida (129.9), Beehive (130.4) Ascellus Borealis (130.9), η Hydrae (131.0), Ascellus Australis (131.4) ε Hydrae (131.9), ι Cancri (132.0), ρ Hydrae (132.4)
'July 29 (210) '30 '31
Alhena 8 9 10
Ka4-7 Ka4-8 (70) Ka4-9 Ka4-10 (*136)
  ζ Hydrae (134.1) Acubens, Talitha Borealis (135.0)  ρ Ursa Majoris (135.6), ν Cancri (136.0), Talitha Australis (136.1)
'August 1 ' 2 (214) '3 '4
Alhena 11 (77) 12 13 Murzim 1 (80)
Ka4-11 (73) Ka4-12 Ka4-13
ω Hydrae (136.8), σ¹ Ursa Majoris (137.0), κ Cancri (137.3), Alsuhail (137.5)  σ² Ursa Majoris (137.6), τ Ursa Majoris (137.7), ξ Cancri (137.8)  Miaplacidus (139.3)
'August 5 (217) '6 '7
Murzim 2 (81) 3 4

I think we should notice the indrawn paw of the Lion at the descending kahi, the τ letter at the ghost, and λ at ariki in 'July 13:

Ka3-1 Ka3-2 Ka3-3 (*108) Ka3-4
Alzirr (105.7), Muliphein (105.8) Wezen (107.1)  θ Gemini (107.6)  
'July 5 (186) '6 '7 '8
Al Tuwaibe' 10 11 12 (52) 13
Ka3-5 (46) Ka3-6 Ka3-7 Ka3-8
Wasat (109.8), ω Gemini (110.1), Mekbuda (110.5) Aludra (111.1)  Gomeisa (111.6), ρ Gemini (112.1), τ Gemini (112.3) Castor (113.4)
'July 9 '10 '11 '12 (193)
Heka 1 (54) 2 3 4
  365 days
  (80 + RA / 24h * 365¼)   Day of culmination  
Atlas 'May 16 (136) 228 'December 31 (365) 135
  56 -3  53 +3
Castor 'July 12 (193) 225 'February 23 (419) 138
New year (?)
Ka3-9 (50) Ka3-10 (*115)
λ Gemini (114.0)  Markab Puppis (114.7), Procyon (114.9)
'July 13 '14 (195)
Heka 5 (58) 6

"Tau (uppercase Τ, lowercase τ ... is the 19th letter of the Greek alphabet. In the system of Greek numerals it has a value of 300 ... In ancient times, Tau was used as a symbol for life and/or resurrection, whereas the eighth letter of the Greek alphabet, theta [θ], was considered the symbol of death." (Wikipedia)

108 days from March 21 was where θ Gemini rose heliacally in rongorongo times. 5 (= 112.3 - 107.6) days later came τ Gemini. It was in 'July 11, Gregorian day 192 (equal to my once estimated number of glyph places on the K tablet).

... The manner of his death can be reconstructed from a variety of legends, folk-customs and other religious survivals. At mid-summer, at the end of a half-year reign, Hercules is made drunk with mead and led into the middle of a circle of twelve stones arranged around an oak, in front of which stands an altar-stone; the oak has been lopped until it is T-shaped.

He is bound to it with willow thongs in the 'five-fold bond' which joins wrists, neck, and ankles together, beaten by his comrades till he faints, then flayed, blinded, castrated, impaled with a mistletoe stake, and finally hacked into joints on the altar-stone. His blood is caught in a basin and used for sprinkling the whole tribe to make them vigorous and fruitful. The joints are roasted at twin fires of oak-loppings, kindled with sacred fire preserved from a lightning-blasted oak or made by twirling an alder- or cornel-wood fire-drill in an oak log.

The trunk is then uprooted and split into faggots which are added to the flames. The twelve merry-men rush in a wild figure-of-eight dance around the fires, singing ecstatically and tearing at the flesh with their teeth. The bloody remains are burnt in the fire, all except the genitals and the head. These are put into an alder-wood boat and floated down the river to an islet; though the head is sometimes cured with smoke and preserved for oracular use. His tanist succeeds him and reigns for the remainder of the year, when he is sacrificially killed by a new Hercules.

The divine names Bran, Saturn, Cronos ... are applied to the ghost of Hercules that floats off in the alder-wood boat after his midsummer sacrifice. His tanist, or other self, appearing in Greek legend as Poeas who lighted Hercules' pyre and inherited his arrows, succeeds him for the second half of the year; having acquired royal virtue by marriage with the queen, the representative of the White Goddess, and by eating some royal part of the dead man's body - heart, shoulder or thigh-flesh.

He is in turn succeeded by the New Year Hercules, a reincarnation of the murdered man, who beheads him and, apparently, eats his head. This alternate eucharistic sacrifice made royalty continous, each king in turn the Sun-god beloved of the reigning Moon-goddess. But when these cannibalistic rites were abandoned and the system was gradually modified until a single king reigned for a term of years, Saturn-Cronos-Bran became a mere Old Year ghost, permanently overthrown by Juppiter-Zeus-Belin though yearly conjured up for placation at the Saturnalia or Yule feast ...