Dilith

Magical shape-memory crystalline material. In its purest form, dilith appears as cubic, amethyst-colored crystals. Weak and brittle on its own, but can be alloyed with practically any substance to give it self-healing properties. Common as a trace mineral, especially in areas with weaker dimensional boundaries. Dilith is often poetically described as 'stability given form'.
Crystalline dilith cold welds on contact with itself. You can't normally make dust or anything out of the pure form, although certain alloys do lend themselves to being powdered. Consequently, the best way to work it into a metal is to fold it, pattern-weld style. It won't just mix/dissolve. Substances with high unset dilith content will exhibit far less weakening from repeated strain and slightly increased hardness, though they have a worse strength to weight ratio.
Note that dilith offers little protection against chemical change. High-dilith iron blades may never lose shape, but will still corrode away with rust.

History

Often found within ores from certain regions, leading to their reputation as being superior quality. Even after its isolation and formal discovery, these ores remained useful, as methods to add dilith to a substance are generally far more expensive than to simply use a source already containing dilith.
Note that dilith's ubiquity is one of the reasons exceptional craftsmen can truly shine: whatever esoteric method or technique used allows the dilith to be magically 'set', granting the finished work dramatically improved durability/lifespan. Conventionally working the metal would not magically set the material in most cases, although certain cultures have stumbled upon more easily repeatable methods that allow for it. Most ore contains at least trace amounts of dilith, although certain regions have significant proportions of the mineral.
The The Sunstone Citadels use dilith in their coinage, owing to their lack of metals (other than iron).
Eventually, dilith saw use as a the primary component of certain alloys used along the edges of high-end knives. While such a large proportion of it to steel results in a relatively brittle alloy, the blades can remain extraordinarily sharp indefinitely even with heavy use. While sword blades and the like make use of it, knives are one of the few applications where the majority of the alloy is dilith.
Ores mined in Epacs (and the surrounding regions) tend to be exceptionally high in dilith content, as the mountains are border to one of the most elementally-aligned regions in the continent (the Molten Desert).
Studying the mechanism for this self-repair was the basis of Epacsi enchantment: basically, a high enough magical energy will define the resting state of the material, storing the object's form in another dimension. From that point on, the material pushes itself to reach that resting state if disturbed. Much early research and development was spent understanding this mechanism and its extradimensional nature, the cast off dilith from arcsteel production being considered a semi-precious stone at best and providing ample specimens for research. While the self-healing mechanism was eventually replicated, the lack of energy input required remained unsolved and considered one of the 'great questions' of the time.

Special Interactions

Higher energy states

Ordinary dilith (dilith-1) 'sets' when exposed to a certain threshold of energy- around as much as is required for stormglass to turn fully liquid. Before reaching this energy concentration, higher energies allow for faster regeneration of material. After this energy concentration, dilith loses its shape-memory properties (instead constantly setting). However, should one push the magical energy concentration far past this, properties loop back aground. This repeats infinitely, alternating every order of magnitude or so. Dilith's number represents the amount of times which the material has crossed into a 'reset' state (as opposed to a 'don't reset' state). Triavanium, for example, contains dilith-3. There are a few alvahedi pieces in the world which contain dilith-3 (see: Thread), but the overwhelming majority are dilith-2. Alvahedi can't actually exist at dilith states below 2 due to its composition. Dilith-2 and higher have never been createzd (in the modern era) outside of controlled lab conditions barring these unique ritual-based alloys.
Extrapolating the properties of dilith to dilith-4 provides a good model for the durability of Artifacts. The energy requirements to test this (especially considering the magical coherency limit putting a lower bound on the minimum size of the experiment) mean that it's impossible verify whether or not this is truly because of any dilith content: 8 orders of magnitude beyond the already considerable energy required to set dilith-1 isn't something that can be created through mundane means. Dilith-3 alvahedi is already famously capable of piercing a god's defenses; to go 2 orders of magnitude further...

Noble Metals

While dilith can fill noble metals, it can't actually be set: energy fed into the metal is converted into adamantine before reaching the dilith. Through what is known in the business as 'superimpositional fuckery', it is possible for enchanters to dilith-reinforce noble metals, but it's not so simple as charging the base material.

Superimposition

Dilith is an example of both major types of superimposition.
Dilith is 'added' to materials by forcing it into loose superimposition in the same space as them. Basically, 'pushing' the dilith away in fourth-dimensional space, and positioning it to overlap with the object's 3D position. Dilith has a natural propensity to 'fall' into the standard fourth dimensional coordinate, so failing to properly attach the materials across this dimension tends to cause it to slide downwards back into regular space.
Dilith's self-repair mechanism works off of longer-distance superimposition, which can't just be treated as 4D space.