3. The reason for the name 'before the dog' probably is that once Procyon was rising earlier than Sirius. We know that by cause of its own movement Sirius (Te Pou) is striving against the general movement forward of the stars to higher right ascension positions, caused by the precession which moves spring equinox gradually backwards earlier and earlier in the year.

... The Sothic cycle was based on what is referred to in technical jargon as 'the periodic return of the heliacal rising of Sirius', which is the first appearance of this star after a seasonal absence, rising at dawn just ahead of the sun in the eastern portion of the sky. In the case of Sirius the interval between one such rising and the next amounts to exactly 365.25 days - a mathematically harmonious figure, uncomplicated by further decimal points, which is just twelve minutes longer than the duration of the solar year ...

If we simplify and say that Sirius stands exactly still compared to Sun, not even changing its position by 12 minutes each year, then we can count 115.9 (the current day number for Procyon) - 102.2 (the current day number for Sirius) = 13.7 days, which amounts to ca 72 * 13.7 = 986 years ago as the date when they could have risen at the same time.

But Sirius is slower to rise than Sun, 12 minutes later for each year. Instead of following the pace of Sun in advancing among the constellations with around 1 day in 72 years, Sirius will proceede at a slower pace. 12 * 72 = 864 minutes is the distance Sirius has lagged in relation to Sun in 72 years.

In 72 years Sun moves ca 24 * 60 = 1440 minutes while Sirius moves ca 1440 - 864 = 576 minutes - ahead among the constellations. Therefore the current distance ahead from Sirius to Procyon, 13.7 days, should take around 13.7 * 72 * 1440 / 576 = ca 2466 years.

I.e., if Procyon does not move against the sky roof of its own (in a way similar to Sirius), then we have to go back in time to at least the time of Herodotos in order to find Procyon rising earlier than Sirius.

I do not know how Procyon moves in relation to the truly fixed stars. But it is not necessary - I think I have 'proven' that once the Little Dog rose before the Big Dog.

I can find information which tells me that Procyon cannot be moving against the fixed stars as quickly as Sirius. Though it could move not much slower. And if it should move in the same direction, compared to how Sirius moves, then we must go back to a time earlier than that of Herodotos in order to find the name Procyon accurate. But Procyon could move in the opposite direction.

If we assume the G text describes prominent stars and their positions in the sky roof - especially their right ascension values - then the stars which move against the background should make it possible to put a date on the G map.

Though to do this we need firm data for several stars and their corresponding glyphs. And we would anyhow not know when the G map was created, because the future (or ancient) positions of the stars can be extrapolated.

We know that Sirius moves. Therefore our preliminary location of Sirius to Ga2-7 can be questioned:

Ga2-1 (*96) Ga2-2 Ga2-3 Ga2-4
Canopus (96.6)      
Ga2-5 (*100) Ga2-6 Ga2-7 Ga2-8
ν Puppis (100.2)   Sirius (102.2) τ Puppis (103.2)

Sirius proceeds ahead among the fixed stars 1 day in approximately 1440 / 576 * 72 = 180 years, a remarkable number which we instantly associate with half 360 days in a year.

But in the G text it ought to move ahead towards Procyon with a pace which we have eastimated as possibly 13.7 glyphs in  ca 2466 years:

12
Ga2-7 (*102) Ga2-20 Ga2-21 (*116) Ga2-22
Sirius (102.2) Castor (114.4) Procyon (115.9) Pollux (117.2)
14

We can now guess why Sirius is not listed among the 10 Tahitian 'star pillars' - it does not stand still. Perhaps Sirius for the same reason is absent from the G text.