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The Babylonian Foundation Stone (Temennu) was in Roman times around 181 days earlier than day 290. 'October 17 (290) - 181 = 109 ('April 19). May 16 (136) - 27 = 109 ('April 19):

BABYLONIAN ECLIPTIC CONSTELLATIONS:
1  1-iku Field measure  τ (Anunitum) Pisces 16.5 April 6 (96)
2 Mahrū-sha-rishu-ku Front of the Head of Ku β (Sheratan), γ (Mesarthim) Arietis 27.4 April 17 (107)
3 Arku-sha-rishu-ku Back of the Head of Ku α (Hamal) Arietis 30.5 April 20 (110)
4 Temennu Foundation Stone η (Alcyone) Tauri 56.1 May 16 (136)

Glyph 355 (probably alluding to the nights of the December solstice) should, according to my interpretation, have been at 'April 17 (107). And 107 + 183 = 290:

Januarius 24 25 26 27 28 (393) 29 (*314)
Gb4-32 Gb4-33 Gb5-1 (354) Gb5-2 Gb5-3 Gb5-4 (128)
MARCH 8 9 10 11 (*355) 12 (436) 13 (72)
no star listed (51) no star listed (52) no star listed (53)

Acrux

no star listed (54) Al Thurayya-27 / Krittikā-3 / Hairy Head-18 / Temennu-4
Atiks, Rana (55.1), CELAENO, ELECTRA, TAYGETA (55.3), MAIA, ASTEROPE, MEROPE (55.6) ALCYONE (56.1), PLEIONE, ATLAS (56.3)
TAU-ONO
May 11 12 (*417) 13 14 15 (500) 16 (136)
4-14 'April 15 16 (471) 17 (107) 18 19 (*29)
NAKSHATRA DATES:
SEPTEMBER 7 8 9 (*172) 10 11 (254) 12
Nusakan (234.0), κ¹ Apodis (234.3), ν Bootis (234.7) θ Cor. Borealis (235.3), γ Lupi (235.6), Gemma, Zuben Elakrab, Qin, ε Tr. Austr. (235.7), μ Cor. Borealis (235.8)

Sirrah

φ Bootis (236.2), ω Lupi (236.3), ψ¹ Lupi (236.7), ζ Cor. Borealis (236.9)  ι Serpentis (237.4), ψ² Lupi (237.5), γ Cor. Borealis (237.7), Unuk Elhaia (237.9) π Cor. Borealis, Cor Serpentis (238.1), Chow (238.6) κ Serpentis (239.3), δ Cor. Borealis, Tiānrǔ (239.5), χ Lupi, (239.6), ω Serpentis (239.7), Ba, χ Herculis (239.8). κ Cor. Borealis, ρ Serpentis (239.9)
Nov 10 (314) 11 12 13 14 15
10-14 'October 15 16 17 (290) 18 19 (*212)
HORA NUI 21 22 (240)  *161 = *236 - *75 24 25 255 - 11 = 244
HORA NUI 25 26 (240) 27 28 29 (*163) TAGAROA URI 1
12
Februarius 11 12 (408) 13 14 15 (46)
Gb5-17 (370) Gb5-18 Gb5-19 Gb5-20 (144) Gb5-21
MARCH 26 (85) 27 28 (*7) 29 30 (454)
no star listed (69) no star listed (70) Tabit (71.7), π² Orionis (71.9) π4 Orionis (72.1), ο¹ Orionis (72.4), π5 Orionis (72.8) π¹ Orionis (73.0), ο² Orionis (73.4), Hassaleh (73.6), π6 Orionis (73.9)
May 29 (149) 30 (*435) 31 June 1 2
'May 2 3 4 5 (125) 6 (*46)
NAKSHATRA DATES:
SEPTEMBER 25 (268) 26 27 28 29 (272)
ζ Herculis, η Tr. Austr. (252.1), η Herculis, β Apodis (252.5) Atria (253.9) Tail-6 ι Ophiuchi (255.3), Grafias (255.4) κ Ophiuchi (256.2), ζ Arae (256.5), ε Arae (256.8), Cujam (256.9)
Wei, η Arae (254.3), DENEBAKRAB (254.7)
November 28 29 (333) 30 December 1 2 (336)
'November 1 (305) 2 3 (*227) 4 5
TAGAROA URI 9 (257) 10 (*178 = *253 - *75) 11 12 (260) 261 = 272 - 11
TAGAROA URI 14 15 (*178) 16 17 (260) 18

I.e., the date Tangaroa Uri 15 in Manuscript E could have referred to a cardinal point half a year after the Pleiades. Then the question remains which calendar together with which precessional age should be chosen (which frame of reference to use). And then remains the task of correlating the dates in Manuscript E with the glyph sequence in the G text.

We can see above that 'October 17 (290) at Gb5-2 is 16 glyphs earlier than my suggested TAGAROA URI 15 (258) at Gb5-18.

... Space and time are a single, related concept in Runasimi [the language of the Inca people], represented by one word, pacha, which can also mean 'world' and 'universe'. The image of time familiar to Waman Puma was static and spatial: one could travel in time as one travels over earth - the structure, the geography, remaining unchanged. To him it does not matter that he shows Inka Wayna Qhapaq, who died in 1525, talking to Spaniards, who did not arrive until 1532. Wayna Qhapaq was the last Inca to rule an undivided empire: he is therefore the archetype, and it must be he who asks the Spaniards: 'Do you eat gold?'

From 'April 17 (107) to day 107 + 183 + 16 = 306 ('November 2) there were 199 days.

It takes time to gnaw a bone until the marrow is reached.

My preceding argumentations leads to a tentative conclusion - the important star at the very beginning could have been Haedus II (η Aurigae) which was at 0h around 11* 71 = 781 years earlier than Hyades II (δ¹ Tauri):

Ga1-11 Ga1-12 Ga1-13 Ga1-14
APRIL 1 (*11) 2 3 (93) 4
Haedus II (75.9) 5h (76.1) μ Aurigae, μ Leporis (77.6)  ĸ Leporis (78.0), RIGEL (78.1), Flaming Star (78.2), Capella (78.4), ο Columbae, τ Orionis (78.8)

Thuban

ε Leporis (76.0), CURSA (76.4), λ Eridani (76.7)
Cursa = λ Eridani and Rigel = β Orionis.
June 4 5 6 (157 = 314 / 2) 7
'May 8 (128) 9 10 (*50) 11
NAKSHATRA DATES:
OCTOBER 1 2 3 (*196) 4 (277)
17h (258.7) Mula-19 Nodus I (260.0), π Herculis (260.7), Ras Algethi (260.8)  Sarin (261.0), ο Ophiuchi (261.4)

Alrisha

no star listed (258) Sabik (259.7), η SCORPII (259.9)
December 4 5 (*259) 6 (340) 7
'November 7 8 9 (*233) 10

Counting 16 days ahead from heliacal Haedus II the star would again become visible at glyph Ga1-27, i.e. in APRIL 17 (80 + 27). Whereas at the opposite (complementary according to Ogotemmêli) side of the sky the 'root' (Mula) had been visible close to the Full Moon already at Ga1-12.

Ga1-27 Ga1-28 Ga1-29
APRIL 17 (107) 18 19 (*29)
6h (91.3) ξ Orionis (92.5) Al Han'ah-4
ν Orionis (91.4), θ Columbae (91.5), π Columbae (91.6)  TEJAT PRIOR (93.4), γ Monocerotis (93.5), κ Aurigae (93.6), κ Columbae (93.8)
June 20 (*91) Solstice 22 (173)
'May 24 (*64) 25 26 (146 = 2 * 73)
NAKSHATRA DATES:
OCTOBER 16 17 (290) 18
Zhōngshān (274.0), π Pavonis (274.6) ι Pavonis (275.1), Polis (275.9)

Menkar

η Sagittarii (276.9)
December 20 (354) Solstice 22
'November 23 (327) 24 (*248) 25

On side b we can similarly count 16 days ahead from Gb5-23, where the rising Haedus II 'fish' in Roman times could have been regarded as the cardinal point 14 * 29½ nights after 0h in the preceding year, i.e. 'May 8 (128) + 365 - 80 = 413. At Cursa a new king had to be created (hakaariki) with his kava ceremonies 50 days after 'March 21:

Februarius 16 17 (413) 18 19 (50)
Gb5-22 (146) Gb5-23 Gb5-24 Gb5-25 (378)
MARCH 31 (*10) APRIL 1 2 (457) 3 (93)
Almaaz (74.7), Haedus I (74.8) Haedus II (75.9) 5h (76.1) μ Aurigae, μ Leporis (77.6)
ε Leporis (76.0), CURSA (76.4), λ Eridani (76.7)
June 3 4 (520) 5 6 (157)
'May 7 8 (128) *414 10 (*50)
NAKSHATRA DATES:
SEPTEMBER 30 (273) OCTOBER 1 2 3
no star listed (257) 17h (258.7) Mula-19 Nodus I (260.0), π Herculis (260.7), Ras Algethi (260.8)
no star listed (258) Sabik (259.7), η SCORPII (259.9)
December 3 4 5 6 (340)
'November 6 (*230) 7 8 9 (313)
TAGAROA URI 14 15 (*183 = *258 - *75) 16 17 (265)
TAGAROA URI 19 20 (*183) 21 22 (265)

... In view of the almost universal prevalence of the Pleiades year throughout the Polynesian area it is surprising to find that in the South Island and certain parts of the North Island of New Zealand and in the neighboring Chatham Islands, the year began with the new Moon after the early morning rising, not of the Pleiades, but of the star Rigel in Orion ...

378 (Gb5-25) - 365 = 13 (Ga1-13). The sequence of heliacal stars has according to my reading not been broken, it has continued without interruption even across from Ga8-26 (229) to Gb1-1 (230).

I introduced such Latin sounding dates as Februarius 20 in order to show what dates would follow from extrapolating backwards in time from Rogo at 0h (March 21) in Gb6-26 (408). For instance: 408 - 379 (Gb5-26) = 29 = March 21 (80) - Februarius 20 (51):

Februarius 20 21 22 (53)
Gb5-26 (150) Gb5-27 Gb5-28 (381)
APRIL 4 (*14) 5 (460) 6
 ĸ Leporis (78.0), RIGEL (78.1), Flaming Star (78.2), Capella (78.4), ο Columbae, τ Orionis (78.8)

Thuban

λ Aurigae (79.0), λ Leporis (79.6), ρ Aurigae (79.7)

Arcturus

Shur-narkabti-sha-iltanu-6
σ Aurigae (80.4), Bellatrix, Saif al Jabbar (80.7), Elnath (80.9)
June 7 8 (*444) 9 (525)
May 11 12 (*52) 13 (133)
NAKSHATRA DATES:
OCTOBER 4 (277) 5 6 (*199)
 Sarin (261.0), ο Ophiuchi (261.4)

Alrisha

ξ Ophiuchi (262.2), θ Ophiuchi, ν Serpentis, ζ, ι Apodis (262.4), ι Arae (262.8), ρ Herculis (262.9) β, γ Arae (263.3), κ Arae (263.5), σ Ophiuchi (263.6)
December 7 8 (342) 9
314 'November 11 *236
TAGAROA URI 18 (*186) 19 20 (268)
TAGAROA URI 23 (*186) 24 25 (268)
TERMINALIA Februarius 24 25 26 27 (58)
Gb5-29 Gb6-1 Gb6-2 (384) Gb6-3 Gb6-4 (157)
APRIL 7 (*17) 8 9 (99) 10 11 (466)
ψ Orionis (81.1), Nihal (81.7) Mintaka, υ Orionis (82.4), χ Aurigae (82.5), ε Columbae (82.6) Al Hak'ah-3 / Mrigashīrsha-5 / Turtle-20 / Kakkab Sar Three Stars-21 / ANA-IVA (9) / Shur-narkabti-sha-shūtū-7 ο Aurigae (85.8), γ Leporis (85.9)

Yang Mun

Arneb, Crab Nebula (83.0, φ¹ Orionis (83.1), HEKA, Orion Nebula (83.2), φ² Orionis (83.6), Alnilam (83.7) Heavenly Gate, ν Columbae (84.0), ω Orionis (84.2),  ALNITAK, PHAKT (Phaet) (84.7)
June 10 (*446) 11 12 13 (164) 14 (530)
'May 14 (*54) 15 (135) 16 17 18 (503)
NAKSHATRA DATES:
OCTOBER 7 (*200) 8 9 (282) 10 (648) 11
Lesath, δ Arae (264.7), Choo (264.9) Al Shaula Ras Alhague (266.1), Sargas (266.3), μ Ophiuchi, π Arae (266.5), Nan Hae (266.6),  ι Herculis (266.7) λ Arae (267.1), Girtab, ο Serpentis (267.6) Kelb Alrai, μ Arae (268.1), Kew Ho (268.6), η Pavonis (268.7), Apollyon (268.9)
 Alwaid, Maasym (265.1), Shaula (265.3), Kuma (265.6), σ Arae (265.9)

Hamal

December 10 11 12 Lucia 14 (348 = 364 - 16)
'November 13 (*237) 14 15 16 (320) 17
TAGAROA URI 21 22 23 24 (*192) 25 (273)
TAGAROA URI 26 27 28 29 (*192) 30 (273)

By counting 16 days ahead from heliacal Haedus II (Gb5-23) we will reach glyph 392, which would have corresponded to APRIL 17 at the time when Hyades II was at 0h. 365 + 11 + 16 = 392. A jump from Roman times (the First Point of Aries) to rongorongo times measured 27 precessional days. June 20 (171), the day before the solstice, corresponded to 'May 24 (144) + 11 + 16:

Februarius 28 Martius 1 2 (61) 3 4 (428) 5 (64)
Gb6-5 Gb6-6 Gb6-7 (160) Gb6-8 Gb6-9 Gb6-10 (392)
APRIL 12 4-13 (468) 14 (104) 15 (*25) 16 (471) 17 (107)
 μ Columbae, Saiph (86.5), τ Aurigae, ζ Leporis (86.6) υ Aurigae (87.1), ν Aurigae (87.2), Wezn, δ Leporis (87.7), Tze (87.9) Ardra-6 / ANA-VARU (8) η Leporis (89.0), Praja-pāti, Menkalinan, Mahashim, and γ Columbae (89.3), π Aurigae (89.4), η Columbae (89.7) μ Orionis (90.3), χ² Orionis (90.5) 6h (91.3)
χ¹ Orionis, ξ Aurigae (88.1), BETELGEUZE (88.3), ξ Columbae (88.5), σ Columbae (88.7)

 Zuben Elgenubi

ν Orionis (91.4), θ Columbae (91.5), π Columbae (91.6)
June 15 16 17 (168) 18 19 20 (171)
'May 19 (*59) 20 (140) 21 22 23 (*63) 24 (144)
NAKSHATRA DATES:
OCTOBER 12 (285) 13 14 15 (*208) 16 17 (290)
Muliphen (269.0), Basanismus (269.5), Pherkard (269.9) Ptolemy Cluster (270.5) Rukbalgethi Genubi (271.1), ξ Herculis (271.5), Etamin, ν Herculis (271.7), ν Ophiuchi (271.8) ζ Serpentis (272.4), τ Ophiuchi (272.9) Winnowing Basket-7 Zhōngshān (274.0), π Pavonis (274.6)
18h (273.4)
NASH (273.7), θ Arae (273.8)
December 15 16 (350) 17 18 19 20 (354)
'November 18 19 (*243) 20 (324) 21 22 (*246) 23 (327)
TAGAROA URI 26 27 28 29 (277) *198 = *273 - *75 31
TAG URI 31 KO RUTI 1 (275) 2 3 4 5 (*199)

Possibly there could here be a 27-day jump in the flow of heliacal stars. However, another interpretation is to let the flow of right ascension day lines together with the relevant stars continue uninterrupted all the way to the end of side b - i.e. to let the implied grid map of star days in the background remain unperturbed by the calendar problems.

Martius 6 7 8 (432) 9 10 11 (70)
Gb6-11 (393) Gb6-12 (165) Gb6-13 Gb6-14 Gb6-15 Gb6-16
APRIL 18 19 (*29) 20 21 (111) 22 23 (478)
ξ Orionis (92.5) Al Han'ah-4 / Maru-sha-pu-u-mash-mashu-8  Furud (94.9) Well-22 no star listed (96) β Monocerotis, ν Gemini (97.0)
 TEJAT PRIOR (93.4), γ Monocerotis (93.5), κ Aurigae (93.6), κ Columbae (93.8) δ Columbae (95.2), TEJAT POSTERIOR, Mirzam (95.4), CANOPUS (95.6), ε Monocerotis (95.7), ψ1 Aurigae (95.9)
Solstice June 22 (173) 23 St John's Eve 25 26
5-25 'May 26 27 28 (*68) 29 30 (150)
NAKSHATRA DATES:
OCTOBER 18 19 20 21 22 (295) 23 (*216)
ι Pavonis (275.1), Polis (275.9)

Menkar

η Sagittarii (276.9) Purva Ashadha-20 Kaus Borealis (279.3) ν Pavonis (280.4), κ Cor. Austr. (280.9)
KAUS MEDIUS, κ Lyrae (277.5), Tung Hae (277.7) φ Oct. (278.1), KAUS AUSTRALIS (278.3), ξ Pavonis (278.4), Al Athfar (278.6)
Solstice December 22 23 Christmas Eve 25 26 (360)
'November 24 25 (329) 26 (*250) 27 28 29
KO RUTI 1 (*200) 2 3 4 5 6 (285)
KO RUTI 6 7 8 9 *204 = *279 - *75 11 (285)

The heliacal stars and dates below could simply be my perceptions instead of what the creator of the text had in mind:

Gb6-17 Gb6-18 (400) Gb6-19 (172)
JANUARY 7 (372) 8 9
no star listed (356) ι Phoenicis (357.3), ι Piscium (357.4), λ Andromedae (357.9) λ Piscium (358.0), Manus Catenata (358.1), Alrai, θ Phoenicis (358.4), κ Andromedae (358.7)
March 12 (436) 13 (72) 3-14
'February 13 2-14 15 (46)
Gb6-20 21 22 23 24 (177)
JANUARY 10 11 12 13 (378) 14
ω Aquarii (359.2), 78 Pegasi (359.5) ψ Andromedae (360.1), σ Phoenicis (360.4) γ¹ Oct. (361.4), φ Pegasi (361.7) Dzaneb (362.4), γ² Oct. (362.8) η Tucanae (363.0), ψ Pegasi (363.1), 32 Piscium (363.2), π Phoenicis (363.4), ε Tucanae (363.6), τ Phoenicis (363.9)
March 15 16 (440) 17 18 19 (78)
'February 16 17 (413) 18 19 20 (51)
Gb6-25 Gb6-26 (408) Gb6-27 Gb6-28 (181)
JANUARY 15 (*300) 16 17 18 (383)
θ Oct. (364.9) Al Fargh al Thāni-25 Uttara Bhādrapadā-27 / Wall-14 χ Pegasi (2.1), θ Andromedae (2.7)
0h (365.25)
Caph, SIRRAH (0.5), ε Phoenicis, γ³ Oct. (0.8) ο Oct. (1.3), ALGENIB PEGASI (1.8)
March 20 (444) 0h 22 23 (82)
'February 21 (52) 22 Terminalia 24 (420)

His map could in principle have been an uninterrupted continuation of the previous sequences:

Gb6-17 Gb6-18 (400) Gb6-19 (172)
Martius 12 (71) 13 3-14
APRIL 24 (114) 25 (480) 26 (*36)
no star listed (98) ν Puppis (99.2), ψ3 Aurigae (99.4), ψ2 Aurigae (99.5)

Gemma

ψ4 Aurigae (100.5), Mebsuta (100.7)
June 27 28 29 (180)
'May 31 (*71) 'June 1 (152) 2 (*63)
NAKSHATRA DATES:
OCTOBER 24 25 (*218) 26 (299)
Abhijit-22 no star listed (282) ζ Pavonis (283.4), λ Cor. Austr. (283.6), Double Double (283.7), ζ Lyrae (283.8)
θ Cor. Austr. (281.0), VEGA (281.8)
December 27 28 29 (363)
'November 30 'December 1 2 (336)
KO RUTI 7 8 (287) 9 (*208)
KO RUTI 12 13 (287) 14 (*208)
Gb6-20 21 22 23 24 (177)
Martius 15 16 17 18 (77) 19
APRIL 27 (482) 28 29 30 (*40) MAY 1 (121)
SIRIUS (101.2), ψ5 Aurigae (101.4), ν Gemini (101.6), ψ6 Aurigae (101.7) τ Puppis (102.2), ψ7 Aurigae (102.4) θ Gemini (103.0), ψ8 Aurigae (103.2), Alhena (103.8), ψ9 Aurigae (103.9) Adara (104.8) ω Gemini (105.4), Alzirr (105.7), Muliphein (105.8), Mekbuda (105.9)
June 30 July 1 2 3 4 (185)
'June 3 (*64) 4 5 6 7 (158)
NAKSHATRA DATES:
OCTOBER 27 (300) 28 29 30 31 (*224)
South Dipper-8 Sheliak, ν Lyrae (285.1), λ Pavonis (285.7)

Atlas

χ Octantis (286.0), Ain al Rami (286.2), δ Lyrae (286.3), κ Pavonis (286.5), Alya (286.6) ξ Sagittarii (287.1), ω Pavonis (287.3), ε Aquilae, ε Cor. Austr., Sulaphat (287.4), λ Lyrae (287.7), Ascella, Bered (Ant.) (287.9)  Al Na'ām-18 / Uttara Ashadha-21
Φ SAGITTARII (284.0), μ Cor. Austr. (284.6), η Cor. Austr., θ Pavonis (284.8) NUNKI (288.4), ζ Cor. Austr. (288.5), Manubrium (288.8), ζ Aquilae (288.9)
December 30 (364) 31 January 1 2 3 (368)
'December 3 4 5 6 (*260) 7 (341)
KO RUTI 10 11 (290) 12 13 14 (*213)
KO RUTI 15 16 (290) 17 18 19 (*213)
Gb6-25 Gb6-26 (408) Gb6-27 Gb6-28 (181)
Martius 20 21 (80) 22 23
MAY 2 (*42) 3 4 (124) 5 (490)
7h (106.5) Wezen (107.1), τ Gemini (107.7), δ Monocerotis (107.9) no star listed (108) λ Gemini (109.4), Wasat (109.8)
no star listed (106)
July 5 6 7 (188) 8 (378 / 2)
'June 8 9 (*80) 10 (161) 11
NAKSHATRA DATES:
NOVEMBER 1 2 3 (*227) 4 (308)
19h (289.2) Al Baldah-19 Aladfar (291.1), Nodus II (291.5), ψ Sagittarii (291.6), θ Lyrae (291.8) ω Aquilae (292.1), ρ Sagittarii (292.6), υ Sagittarii (292.7)
λ Aquilae (Ant.) (289.1), γ Cor. Austr (289.3), τ Sagittarii (289.4), ι Lyrae (289.5), δ Cor. Austr. (289.8) AL BALDAH, Alphekka Meridiana (290.1), β Cor. Austr. (290.2)
January 4 5 (370) 6 7 (12 * 31)
'December 8 9 10 (344) 11 (*265)
KO RUTI 15 (*214) 16 (295) 17 18
KO RUTI 20 (*214) 21 (295) 22 23