Id

What this is

An Id is a candidate key: an injective, content-independent name that denotes exactly one object within a scope.

The mathematical invariant comes from the relational model (Codd 1970). In a relation R over attributes A₁, …, Aₙ, a superkey is a subset K ⊆ {A₁,…,Aₙ} whose values jointly determine the tuple — no two distinct tuples agree on all K-values. A candidate key is a minimal superkey. An id in a single-attribute key: a single attribute K = {A_k} whose value uniquely determines the object within R.

In model-theoretic terms: an id is a constant symbol c in the language L with a fixed interpretation c^M = a in model M. The naming function n: Ob → Names must be injective within scope: no two distinct objects receive the same name. The id denotes a without saying anything about a — that is the job of Description.

Three properties that make a symbol an id rather than just a label:

1. Uniqueness within scope — n is injective: n(a) = n(b) implies a = b in the scope.
2. Stability — n(a) is invariant under changes to a’s content. If the object’s properties change, its id does not.
3. Opacity — the id does not encode the object’s properties. An id like doc-42 is opaque. An id like senior-english-document conflates naming with description — it encodes properties that may become false.

Stability and opacity together enforce the separation of concerns between addressing and characterizing: you cite an object by its id, you understand it by its description.

Id in category theory

In a category C, objects are identified only up to isomorphism — there is no canonical name for an object, only its universal properties. An id breaks this identification: it assigns a canonical representative to each isomorphism class. This is exactly what condition 2 of U_G requires — isomorphism closure gives canonical representatives, and an id names them.

In URI theory (RFC 3986): a URI is an id for a resource — a string that names it uniformly, independently of its current location or representation. The key requirement is that the URI denotes the resource, not describe it.

In this system

An id is the frontmatter id: field of a spec file — a lowercase hyphenated string that names the entity within the spec locale. The defined term (RelationalConceptPackage) is the name of the concept; the id (relational-concept-package) is the canonical address of the file that specifies it.

Open questions

• Whether ids must be globally unique across all locales or only locally unique within a scope — equivalent to asking whether the naming function is a global injection or a family of local injections.