Jack

When he uncovered the black circle (backstory), he had a suspicion what the device might be, if only because of the apparating, early morning rice parcels.

Via lucky slip of finger, he turned on the 'new Guardian password sequence', and guessing from the runes that confronted him, entered his astrological date of birth.

This matched with his DNA record, and he was accepted by the device as being the next Guardian of the Second.
 

Ælkræleinnoire

Kay presents a quandary, when all others have been inducted to position by the Core, and she apparently is already accepted.

Later it become obvious she needs to be inducted by the Core to access higher functions.

So, why does Kay have access?

The reason was that she wore a second's Ring of Oma, which to some part, overruled the Core of Taris' ship. Put simply, she was recognised as being a part of the controlling team, but not inherent of that particular spacecraft.
 

n'Gnung

n'Gnung becomes the first person Jack empowers as a ring bearer. A willing guinea pig, n'Gnung is accepted, and the team grows quickly.
 

Western Astrology

This page is not especially about Astrology, but relates to how to identify one individual in all of Space-Time. This includes, which planet, which solar system they were born in.

So, how does one do that?

Each person is born at a precise location in space and time. This point can be assigned using astrological techniques, if graded extremely finely.

This is used throughout the trilogy to empower ring bearers. Jack was the first mentioned, when he entered his Sun Sign, Mid Heaven, and Rising Sign. Normally these are compared with existing DNA samples, but in Jack's case, there were none, so his DNA had to be a precise match for his entered space-time co-ordinates of birth; he also needed to possess the Signature of The Guardian.
 

The modern, and so traditional way of representing the Western signs of the zodiac is replicated above. It always begins with Aries, and ends with Pieces, although the latter may be divided into two parts.

There exist other forms of representing the zodiac, one referenced by Jack's Astrologer. This referred to a more ancient pictorial of the signs of the zodiac, which is reproduced below.

Runes were created as a writing system by the Ancestors, and were far more complex than those known of circa the first century BC. They also include other symbols, of which Astrological and Alchemic symbols are included. Later discovered by the Last, they were adapted and used.
 

Jack, like many of his kind, had dabbled with Astrology, enough to know his three main signs; Sun Sign, Mid Heaven, and Rising Sign: Aries, Pisces, and Scorpio respectively. They are important in that order.

Once, for a laugh on a day out, he had his fortune read by an Astrologer. Although the reading he dismissed as the ramblings of a charlatan, a money making scam, some of what she told him, remained with him for life.

Later, Jack wrote down what she had told him, which is replicated below
 

Jack's astrology reading:

“The Twelve signs represent the Twelve Ages of Man.
You as Aries are the child of the Universe, and subsequently know no fear.
Divide the number 12 into the average age of your forefathers, and you will know how long within each age the sign rules in your own world.
Today that would be say, seven years - So Aries is that of the life of a child up until seven years of age.

Your Mid-Heaven, Pisces is of the other extreme.
They have experienced all of life and know its virtues and deceit.
Inherently, Pisces have the oldest heads of us all; but yet they are just as fallible as you my inquisitive Ram. Reason, understanding, or wisdom, are not inherently related to age.
Know that Pisces have both feet planted firmly on the ground, and directly opposite your Sun Sign that signifies The Head, and Oh so many bright ideas.

Scorpio should never be with this pairing.
Yet this is your own Rising sign, indicating you will keep probing and poking until a point of resolution is reached.
I cannot imagine how your life will evolve—you will necessarily ask far too many questions in the places that secrets lay buried for all time.
You would die young, except that Pisces is your Mid Heaven, and wily Aries as your guide in life. It does not make any sense at all, unless you die and are reborn somehow? Remember:
Scorpio is the Finder & Keeper of Secrets.”

From the above, it is easy to discern how the Ancestors revised their extant space-time co-ordinates to suit life on Gaia. We call it Astrology, they called it an individuals birth-stamp. A record of a persons uniqueness, as expressed in their singular DNA, that matches precisely, their time and location of birth.

The symbols used are unique to one planet, and very different in other solar systems. For the Ancestors, it was all but foolproof.

References
http://karenswhimsy.com/zodiac-symbols.shtm
http://www.rodurago.net/en/index.php?site=details&link=aries
 

Ancestor's Origin

The Ancestors, developed on Centaurea, a planet orbiting Proxima Alpha, the smallest Sun of the three star Alpha Centauri system.

They fled their star when the Aleutian-Hallion Alliance came to exterminate their species. To ensure the utter extinction of homo sapien atavus, they not only destroyed the planet, but turned their aging sun into a red dwarf.

The aggressors did not stay to monitor, and many fled the star system, some heading for our solar system.