Astral coordinates
From Mizahar Lore
Astral coordinates are a series of numbers that allow a Summoner to open a gateway to a specific world. They represent a path for traveling from one world to another.
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Overview
Each world is a planet in the universe of Mizahar. Astral coordinates are a string of numbers that describe a path from a starting world to a destination world. The major problem in establishing a path is that the worlds' positions in space relative to each other change all the time as planets revolve around their suns and those suns in turn revolve around other systems. If one were simply to write down a direction and an angle, such as when shooting an arrow, this would only work at a specific time.
Astral coordinates, on the other hand, are universally valid. They describe a path in terms of Djed emissions from the specific world, translated into numbers. If the world is very distant, its emissions may be too weak to be accessible from Mizahar; in this case, the path must be described as a series of hops with one or more stops in between.
Measurement
A world's emissions can be measured through sophisticated jewelcraft and Alchemy, which can also measure them from the corpse of a native creature or substantial amounts of materials from that world. From there, either the world can be accessed directly or, if it is too distant for that, it is just a matter of trial and error to combine that world's emission signature with known paths and check if it is possible to open a Summoning gateway.
The process for measuring emissions makes use of sixteen suitably cut Infinitite crystals, each larger than the next. The smallest is less than nail-sized, whereas the largest is taller than a grown man. When these crystals are laid on the material they are to measure and gently hit with a small hammer, they will produce a sound of varying intensity. An expert can rate the sound with a number from 0 to 9. Taken together, from the smallest crystal to the largest, these 16 numbers will form something like "0491093550312866". This is the world's signature.
Interestingly, the procedure is fruitless when attempted on Mizahar itself. All crystals produce no sound, though astral coordinates "0000000000000000" will not open a gateway to Mizahar. For this reason, the world of Mizahar is considered to have no astral coordinates.
Example
The world of Fyrden has very well known astral coordinates - "6701984710485453". Being a world close to Mizahar, this signature is enough to make Summoning possible. The barbaric world of Kavaki is quite distant and can be accessed through Fyrden, so its full coordinates are "6701984710485453-0491093550312866".
Astral logs
Summoners usually learn coordinates by heart, however astral logs containing rare coordinates are highly prized. As Summoning took a major hit with the Valterrian, much knowledge has been forgotten, and logs may be the only way to regain access to a number of lost worlds.