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6. Once the Gemini constellation must have dominated the time of the June solstice. And in rongorongo times Rei in Ka2-10 presumably was at the day after 'June 21, when the first star (η) of the pair at Castor's left foot rose heliacally. His left foot coincided with the days of St John:

The feet of Gemini:
Castor left Tejat Prior η Gemini 3.31 22° 31′ N 06h 12m 94.4
Tejat Posterior μ Gemini 2.87 22° 32′ N 06h 20m 96.4
right   ν Gemini 4.13 20° 13′ N 06h 45m 102.6
Pollux right Alhena γ Gemini 1.93 16° 27′ N 06h 53m 104.8
left Alzirr ξ Gemini 3.35 12° 54′ N 07h 01m 106.7
Ka2-10 (29) Ka2-11 Ka2-12 Ka2-13 Ka2-14
Tejat Prior (93.4) κ Aurigae (93.6) Furud (94.9), Tejat Posterior, Mirzam (95.4) Canopus (95.6), ψ1 Aurigae (95.9)  
'June 22 '23 (St John's Eve) '24 (St John's Day) '25 '26 (177)
Albatain 10 11 12 13 (40) Al Tuwaibe' 1

12 days (= 105.7 - 93.4) after η Gemini the 'Button' star - Alzirr, ξ, at the left foot of Pollux - could have been the 'Tree' which put a definite end to the old year:

A new year could thus have begun with 'July 5 in day 185 + 1 counted from 'January 1. Yet, evidently another kind of new year could begin later, after the death of Castor:

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
Atlas - Castor 58 days 227 (π) 355 365
'July 13 (194)
Procyon - Vega 168 days
- Altair 18 days 128
- Menkar 110 days
- Atlas 10 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 (?)

The pure elbow ornament at τ Gemini (112.3) maybe primarily illustrates how here (where 13 * 29½ / 2 = 191¾) the lunar synodic cycle is divided in 2 halves like a pair of empty sea-shells (where only the whispers of its former inhabitant can be heard).

Pure

Cowrie (Cypraea caput draconis); pure vaka, another type of cowrie, which can float on the sea like a diminutive boat (vaka). Vanaga.

1. To pray, to supplicate, invocation, prayer; hare pure, church, chapel; tae pure, irreverence; purega, prayer P Pau., Mgv., Mq., Ta.: pure, to pray. In Samoa, Tonga, Niuē, Futuna, Uvea, pule means to command. 2. A shell T. P Pau.: hakapurepure, to dye, to color. Mq.: pué, the porcelain shell. Ta.: pure, a mark. Purepure, spotted, dappled; ragi purepure, dappled sky. Purepurea, spotted. P Pau.: hakapurepure, to dye, to color. Mgv.: purepure, printed cloth; akapurepure, to paint in different colors. Mq.: puépué, covered with pale scars. Ta.: purepure, spotted, dappled. Churchill.

Pureva, rock, stone (small enough to be thrown by hand). Vanaga. Pureva, to throw a stone. Ta.: Pureva, to be on the eve of going. Ha.: puleva, to float here and there. Churchill.

Pau.: Pure-hiva, a butterfly. Mgv.: pure-rehue, id. Ta.: pure-hua, a moth. Mq.: pure-hua, id. Ma.: pure-hua, id. Churchill.

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)

Such a new year could have been defined by Rei at χ Carinae, which rose heliacally 120 days from 'March 21 in Gregorian day 200. Or it could have been defined by the beginning of the Alhena manzil, because Ka3-18 is number 59 (= 2 * 29½) and because there is an obvious Sign of division with a new little entity ahead:

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

The last Gemini star (χ) rose heliacally at the end of line Ka3. I think glyphs, stars, and dates fit so well together that we ought to formulate a hypothesis:

Firm evidence, from Rei in Ka2-10 ('June 22) to the end of line Ka3, indicates we should add 64 to the glyph numbers in K in order to reach the RA dates.

There is also evidence 64 should be used earlier, at least from 'June 6 in Gregorian day 157 (= 314 / 2):

(4) (1)
Ka1-11 (*75) Ka1-12 *Ka1-17 (13) *Ka1-18 (14)
Almaaz (74.7), Haedus I (74.8) Haedus II (75.9), ε Leporis (76.0), Cursa (76.4) λ Eridani (76.7) μ Leporis (77.6), ĸ Leporis (78.0), Rigel (78.1), Capella (78.4)
'June 4 '5h (76.1) 'June 6 (157) '7
Pleione 5 6 (20) Pleione 7 8 (22)

Only visible glyphs should be counted.

The simplest hypothesis is then to say this rule of 64 governs not only all the glyphs on the K tablet, but that we should also add 64 when counting RA days for the glyphs on the G tablet (and then not to count the glyph numbers from Gb8-30 but from Ga1-1).