A continuation of this thread, before it got derailed.
Invisig0th gave good advice here, comparing the githyanki to silver swords rather than a generic steel sword. Although Gith herself almost certainly did not wield a silver sword for most of her career, the silver sword is still the most powerful metaphor the githyanki have. They could interpret the sword of Gith as having the same metaphorical qualities as a silver sword.
Try: "The People were created by the strength of the Sword; they are like the Sword, flexible enough to bend but never break, and cut that which cannot otherwise be cut."
The racial modifiers for githyanki are +2 Dex, +2 Con - tough but flexible, like a silver sword. The sword can also be a metaphor for the cutting edge of a githyanki's intellect. They are not smarter than humans, but in intellect they definitely shine above their githzerai cousins.
They also have a penalty to wisdom. They prefer acting swiftly, and view consideration as weakness. The Sword acts without thought. The Sword is thought, and thought is best manifested as action. The illithids considered too much, and this was their weakness. The followers of Zerthimon hesitated because they were overthinking what must be done. They were weak, but the children of Gith were strong, and continued to push forward. Githyanki are intelligent, but not thoughtful.
I think most of your standards are very good. I have an issue only with this:
As this seems more of a githzerai characteristic. Githzerai are taciturn and silent. Githyanki are much more loquacious.
I would also suggest that maybe githyanki call themselves something other than the People, as that seems pretty distinctively a githzerai thing. Maybe something like the Race - similar, but perhaps a little more ominous, as it has more racist connotations.
Remember the psychology of githyanki - they live in a plane outside of Time. Time, for them, is something that happens elsewhere. The past and future only exist on other planes.
The plane of the githyanki is a formless plane of pure thought. Nothing is truly substantial there, though it may seem like it; form is an illusion.
Githyanki are highly psionic. Their life is experienced as a relationship between the pool of psychic energy within them and the pool of similar power flowing through the void outside them.
Finally, it might be good to consider exactly what happened when Gith united the race. How did she discover the power of the sword? How did she discover the power of unity? How did she meet Zerthimon and Vlaakith I? What were her motivations in bargaining with Ephelomon and Tiamat? Those who wrote this text probably didn't know the answers to any of this, but what did they believe?
Finally, this doesn't have to be the be-all, end-all of githyanki philosophy. It might be one of many such texts, so there's no reason to include everything I've mentioned.
Just throwing it out there but what's wrong with the sharp edged codex covering similar events to those in the unbroken circle? It would give a very different take on the events I imagine (showing the weakness of others and the superiority of the Githyanki's) but it could cover many similar events. As with the two races, the differences are in the details and the spin put on the events, their philosophies probably could be reconciled (but probably won't be).
I think that this line of thinking could have a lot to offer.
Also, could there be a penalty for failing to successfully learn/open a new level of the text? A sort of 'the weak will be punished'/'only the strong survive' aspect to the teaching? maybe it cuts those who don't pass the required int/dex check?
"We're making a better world. All of them, better worlds." - Anonomous Harmonium Officer