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The Auriga Charioteer had lost his horse

and - we should remember - the list of the Hindu nakshatra stations was beginning with the Head of a Horse (the pregnant sign of a dead favourite we were taught by the famous Godfather movie):

ARIES:
1 Ashvini β and γ Arietis Horse's head April 17 (107)
wife of the Ashvins Sheratan and Mesarthim
2 Bharani 35, 39, and 41 Arietis Yoni, the female organ of reproduction May 1 (121)
the bearer  Musca Borealis
GEMINI:
7 Punarvasu α and β Gemini Bow and quiver July 12 (193)
the two restorers of goods Castor and Pollux

In Roman times the First Point of Aries was the name for the pair Sheratan and Mesarthim, and since then they had moved ahead in the Sun calendar with around 27 right ascension days. 80 (0h) + 27 = 107 = April 17 = 'March 21 (80) + 27.

Maybe The Dark Rat (Te Kioe Uri) was 29 right ascension days earlier than day 123 (Te Piringa Aniva) = 58 glyphs earlier than Te Pei, and 3 * 29 = 87 days earlier than Sirius at Te Pou. 181 - 87 = 94 ("April 4).

Nga Kope Ririva Tutuu Vai

A Te Taanga

Pu Mahore

 A Hau Maka O Hiva

Poko Uri

 A Hau Maka I [Sic!] Hiva

Te Manavai

A Hau Maka O Hiva

Te Kioe Uri

Te Piringa Aniva (123 = 152 - 29)

Te Pei (152 = 181 - 29)

Te Pou (181)

Hua Reva

Akahanga

Hatinga Te Kohe

Roto Iri Are

Tama He Ika Kino He Ihu Roroa

One Tea

A Hau Maka O Hiva

Hanga Takaure

Poike

Pua Katiki

Maunga Teatea

Mahatua

Taharoa

Hanga Hoonu

Rangi Meamea

Peke Tau O Hiti

Maunga Hau Epa

Oromanga

Hanga Moria One

Papa O Pea

Ahu Akapu

Te Pito O Te Kainga

However, another possibility is that Piringa Aniva referred to Mirach in Andromeda:

"Piringa-o-Tautu; the Tuamotuan name for Beta Andromedae. It is described as a medium bright star east of Takurua-tuki-hanga-ruki, which Emory identifies with Alpha Andromedae." (Makemson)

te kihikihi o te henua - kua haga hia kua pua te vero te henua kiore - te henua
*Ca14-12 *Ca14-13 *Ca14-14 *Ca14-15 (378) *Ca14-16 *Ca14-17
Sept 29 30 Oct 1 2 3 4 (277)
CLOSE TO THE FULL MOON:

ξ Phoenicis (9.0), ρ Tucanae (9.1), DENEB KAITOS (Tail of the Sea Beast) = β Ceti, η Phoenicis (9.4), AL NITHĀM (String of Pearls) = φ¹ Ceti (9.6)

*333.0 = *374.4 - *41.4
ACHIRD (Woman with Luminous Rays) = η Cassiopeiae (10.7)

Legs-15 (Wolf)

ν Andromedae (11.0), φ² Ceti (11.1), ρ Phoenicis (11.2), η Andromedae (11.4)

*335.0 = *376.4 - *41.4

CIH (Whip) = γ Cassiopeiae, λ Tucanae (12.4), φ³ Ceti (12.6), μ Andromedae (12.8)

*12.4 + *365.0 -*41.4 = *336.0 (= 7 * 48)
φ4 Ceti (13.2) no star listed (14)

... At the beginning of 44 B.C. - when Ceasar was still alive - the Senate decided to raise statues of him in all the temples and to sacrifice to him on his birthday in the month Quintilis, which in honour of him was renamed July. He was raised to the status of a god (among the other gods of the state) under the name Jupiter Julius. Marcus Antonius, who this year was consul together with Caesar, became high priest and responsible for the ceremonies. In the middle of February, at the time of the old feast of Lupercalia [Lupus = Wolf], he ran around naked and whipped the Roman ladies with thongs made from goat-skin [februa], in order to promote their fertility ...

March 30 31 April 1 (91) 2 3 4
'March 3 4 (63) 5 6 7 8
"Febr 17 (413) 18 19 (50) 20 21 22
te honu paka te henua honu kau te mata te honu kua heheu
*Ca14-18 *Ca14-19 *Ca14-20 *Ca14-21 (384) *Ca14-22 *Ca14-23
Oct 5 6 7 (280) 8 9 10
CLOSE TO THE FULL MOON:

1h (15.2)

β Phoenicis (15.1), υ Phoenicis, ι Tucanae (15.6), η Ceti, ζ Phoenicis (15.7)

Al Batn Al Hūt-26 (Belly of the Fish) / Revati-28 (Prosperous) / 1-iku (Field Measure)

MIRACH (Girdle) = β Andromedae, KEUN MAN MUN (Camp's South Gate) = φ Andromedae (16.0), ANUNITUM = τ Piscium (16.5), REVATI (Abundant) = ζ Piscium (16.9)

 REGULUS (α Leonis)

ν Phoenicis (17.4), κ Tucanae (17.6)

*342 = *383.4 - *41.4 = 421 - 80 + 1
no star listed (18) ADHIL (Garment's Train) = ξ Andromedae (19.3), θ Ceti (19.7) KSORA (Knee) = δ Cassiopeiae (20.1), ω Andromedae (20.6), γ Phoenicis (20.8)
April 5 6 7 8 (463 = 365 + 98) 9 10 (100 = 465 - 365)
'March 9 10 11 12 (436 = 463 - 27) 13 14 (73)
"Febr 23 (Terminalia) 24 (55 = 123 - 68) 25 26 27 28 (100 - 41 = 59)

... The leap day was introduced as part of the Julian reform. The day following the Terminalia (February 23) was doubled, forming the 'bis sextum - literally 'double sixth', since February 24 was 'the sixth day before the Kalends of March' using Roman inclusive counting (March 1 was the 'first day'). Although exceptions exist, the first day of the bis sextum (February 24) was usually regarded as the intercalated or 'bissextile' day since the third century. February 29 came to be regarded as the leap day when the Roman system of numbering days was replaced by sequential numbering in the late Middle Ages ...

PISCES:
28 Revati ζ Piscium Fish or a pair of fish, drum April 6 (96)
prosperous  Revati
ARIES:
1 Ashvini β and γ Arietis Horse's head April 17 (107)
wife of the Ashvins Sheratan and Mesarthim
2 Bharani 35, 39, and 41 Arietis Yoni, the female organ of reproduction May 1 (121)
the bearer  Musca Borealis

In which case Te Piringa Aniva might have been counted as the day after Terminalia (54 = 31 + 23), viz. Bissextum (55 = 420 - 365) where Regulus culminated and where Sirrah (the Navel of the Horse) became visible again after its close encounter with the Sun.

55 ("February 24) - 29 = "January 26 (possibly Te Kioe Uri):

e toru gagata, tuhuga nui, tuhuga roa, tuhuga marakapa* - ma te hokohuki te tapamea - te kihikihi

* Jaussen: kapa chant.

te vaha erua - te maro tagata kara te roturotu - te maro ka pu te niu - mai tae huki hia ka pu te niu

Rotu. To throng, to flock, to crowd, used of people gathering in great numbers for a feast, for mourning, for working, etc. he-rotu, he-tatagi, the mourners are flocking together; he-rotu i te umu, they are crowding around the earth oven; he-rotu, he aga, they come to work in throngs. Roturotu, to clap hand, to applaud. Vanaga. Roturotu: 1. To clap, to wink. PS Pau.: rotu, to strike the water. Mgv: rotu, to beat the sea in order to frighten fish into a net, to beat a drum. Mq.: ótu, to drive fish into the seine. Ta.: rotu, to strike. Sa.: lotu, to make a hollow sound in the water with the hand. 2. To take to pieces. Churchill.

... in the ceremonial course of the coming year, the king is symbolically transposed toward the Lono pole of Hawaiian divinity ... It need only be noticed that the renewal of kingship at the climax of the Makahiki coincides with the rebirth of nature. For in the ideal ritual calendar, the kali'i battle follows the autumnal appearance of the Pleiades, by thirty-three days - thus precisely, in the late eighteenth century, 21 December, the winter solstice. The king returns to power with the sun. Whereas, over the next two days, Lono plays the part of the sacrifice. The Makahiki effigy is dismantled and hidden away in a rite watched over by the king's 'living god', Kahoali'i or 'The-Companion-of-the-King', the one who is also known as 'Death-is-Near' (Koke-na-make). Close kinsman of the king as his ceremonial double, Kahoali'i swallows the eye of the victim in ceremonies of human sacrifice ... In the deep night before the image [of Lono] is first seen, there is a Makahiki ceremony called 'splashing-water' (hi'uwai). Kepelino tells of sacred chiefs being carried to the water where the people in their finery are bathing; in the excitement created by the beauty of their attire, 'one person was attracted to another, and the result', says this convert to Catholicism, 'was by no means good'. At dawn, when the people emerged from their amorous sport, there standing on the beach was the image of Lono. White tapa cloth and skins of the ka'upu bird hang from the horizontal bar of the tall crosspiece image. The ka'upu is almost certainly the albatross, a migratory bird that appears in the western Hawaiian chain - the white Lanyon albatross at Ni'ihau Island - to breed and lay eggs in October-November, or the beginning of the Makahiki season ...

Ca13-11 (354) Ca13-12 Ca13-13 Ca13-14 → π Ca13-15
CLOSE TO THE FULL MOON:
March 9 10 11 (70 = 435 - 365) 12 13
ο Cephei (353.3), KERB (Bucket Rope) = τ Pegasi (353.6)

κ Piscium (354.2), θ Piscium (354.4), υ Pegasi (354.9)

*313.0 = *354.4 - *41.4
ο Gruis, SNOWBALL NEBULA = NGC7662 Andromedae (355.0), τ Oct. (355.3) no star listed (356) ι Phoenicis (357.3), ι Piscium (357.4), λ Andromedae (357.9)

*316.0 = *357.4 - *41.4

'Febr 7 8 (365 + 39 = 404)  9 (40) 10 11
"Jan 24 25 26 (= 55 - 29) 27 28
DAY 353 354 (= 434 - 80) 355 → solstice 356 357

... τ, 4.5, with υ, was Al Sufi's Sa'd al Na'amah, which Knobel thinks should be Al Na'āim, the Cross-bars over a well; but they also were known as Al Karab, the Bucket-rope. The usual titles for τ - Markab and Sagma or Salma - are from Bayer, but the last two should be Salm, a Leathern Bucket ...

... With α Andromedae [Sirrah → Navel] and γ Pegasi [Kerb], as the Three Guides, it [Caph → Phoenician Kaph, Hand] marks the equinoctial colure, itself exceedingly close to that great circle; and, being located on the same side of the pole as is Polaris, it always affords an approximate indication of the latter's position with respect to that point. This same location, 32º from the pole, and very near to the prime meridian, has rendered it useful for marking sidereal time. When above Polaris and nearest the zenith the astronomical day begins at 0 hours, 0 minutes, and 0 seconds; when due west the sidereal time is 6 hours; when south and nearest the horizon, 12 hours, and when east, 18 hours; this celestial clockhand then moving on the heavenly dial contrary to the motion of the hands of our terrestrial clocks, and at but one half the speed ...

Given the idea of Water connected with a Rat it seem reasonable to connect Te Kioe Uri (the Dark Rat) with a Water Bucket.

... In China, with Capricornus, Pisces, and a part of Sagittarius, it [Aquarius] constituted the early Serpent, or Turtle, Tien Yuen; and later was known as Hiuen Ying, the Dark Warrior and Hero, or Darkly Flourishing One, the Hiuen Wu, or Hiuen Heaou, of the Han dynasty, which Dupuis gave as Hiven Mao. It was a symbol of the emperor Tchoun Hin, in whose reign was a great deluge; but after the Jesuits came in it became Paou Ping, the Precious Vase. It contained three of the sieu, and headed the list of zodiac signs as the Rat, which in the far East was the ideograph for 'water', and still so remains in the almanacs of Central Asia, Cochin China, and Japan ...