Far Fairlian Magic

Every Far Fairlian, including those born on Earth, have a metaphysical connection to their own world that is most commonly conceptualized as a 'life-thread' or 'silver cord." This connection has been dubbed the sutratma. Each sutratma is both individual and recognizable by other sutratma; each also serves as an organ for percieving other sutratma. It can also be suppressed or 'tucked away' when one does not wish to be recognized.

Manifestation

Because the Far Fairlians learn to manipulate their sutratma early in childhood alongside learning language, the two are often tightly linked, and many common magics are invoked with both speech and hand-signs. Specific workings, what we might call 'spells,' are called 'knots'.
There are a number of Core Knots that almost every Fairlian absorbs through cultural osmosis. The development of each one save the most recent has been followed around a thousand years later by the self-destruction of Fairlian civilization. (The Dimensionality Core Knot was developed about 3700-5000 years ago.) These Core Knots generally require conscious effort and some degree of skill to use above a very immature level, and each one is the subject of an entire academic field.
The well-known Core Knots, in order of development, are:

1. illusion or 'light'
2. heat or 'fire'
3. pressure, also known as 'stone'
4. penetration and symbolic weapons (pain, pleasure, and taste)
5. grace and entanglement (ranged communication)
6. dimensionality: movement specializations, dimensional pockets and 'luck' (fate programmers)

There are also less commonly known Medial knots, some of which are significant to linger in the general unconscious. With a few high profile and misleading exceptions, Peripheral knots are only known to skilled professionals; they're usually cited on professional credentials along with any knightly orders.
Most Fairlians can also conjure at least a few things: a favorite food, developed in childhood and traditionally a fruit, and a symbolic weapon, developed in early adulthood, are the most commonly known. While the symbolic weapons usually have only a temporary existence, the favorite food is both real and nutritive. Energy is required for this creation but only a small seed of energy from the conjurer. They push that energy through a shape they've formed their sutratma into, which catalyzes a reaction within the worldsoul that pulls a fruit into their hand. After that, they eat or trade it.
While a single conjuration is not costly, repeated conjurations across a day will each be harder than the last. Many theories to account for this have been advanced, but none have ever taken the lead over the others. (Occasionally, this question has caused holy wars.) The average Fairlian adult (not a specialist) can conjure about four times between dreamful sleep.
Specialists generally can use a particular Core Knot more often. Medial Knots have their own specialists and may be pursued as hobbies. Peripheral Knots, with a few prominent exceptions, are industry-specific knots that are often noted on a professional's credentials alongside any knightly orders they're in. In addition, anybody who works extensively with their sutratma develops a few personal knots (often including a special form of knot known as 'the familiar'.)
Mastery of one Core Knot entitles one to call themselves a Rank 1 mage, by the laws of the land. Mastery of 5 knots makes you an Archmage, at Rank 5. It's said that Mage ranks go up to 9.
Everyone who studies more than the fundamentals is familiar with the Voices, which are urges to do apparently random, usually harmless acts which manifest as a part of a deeper understanding of Dimensionality. Most of those so afflicted are agreed that by indulging such urges, they're assisting another version of themselves they cannot otherwise meet, known as 'Echoes'. The more Echoes one can overlap with, the more flexible one's knots can be, which serves as an incentive toward an adventurous life.

Localization

It's important to a historical understanding to realize we have clear records dating back to when entanglement and dimensionality were common Medial knots, and it is hypothesized that once they may have been Peripheral or even personal knots; certainly dimensional tapping was once only done by highly trained harbingers, and now it is performed casually by adolescents.

While imagining the sutratma as a string is useful both in discussion and teaching, it lacks several associated traits. Notably, there is no known way to cut the sutratma, and it has an imaginary length. It can, however, be passed to another, stolen, restrained, and snap back.

When asked how such disparate evolutionary paths could wind up producing two species who can, as my grandma said, 'play each other on TV,' noted Fairlian researcher Bethel Organzaza leaned forward and said, "Fate manipulation, my dear lady. Our stars aligned."
Later that night, he explained to me that Earth had often figured in Fairlian children's stories as a place full of mind controlled people, and that scholars had long known the reason for this: many different calculations had revealed that such a place as Earth _had_ to exist. So when they decided to look for extradimensional help, they chose a familiar story as their guidepost.

Don't play games of dice with a Fairlian. It doesn't take much skill at all to control apparently random things, sometimes on an instinctive level