UOR Schema

IRI: https://uor.foundation/schema/
Prefix: schema:
Space: kernel
Comment: Core value types and term language for the UOR ring substrate. Defines Datum (ring element), Term (syntactic expression), and the Ring container.

Imports

https://uor.foundation/u/

Classes

Name	Subclass Of	Disjoint With	Comment
`Datum`	`Thing`	`Term`	An element of the ring Z/(2^n)Z at a specific quantum level n. The primary semantic value type. Disjoint from Term: datums are values, terms are syntactic expressions that evaluate to datums.
`Term`	`Thing`	`Datum`	A syntactic expression in the UOR term language. Terms are evaluated to produce Datums. Disjoint from Datum.
`Triad`	`Thing`		A three-component structure encoding an element's position in the UOR address space: stratum (ring layer), spectrum (bit pattern), and glyph (Braille address).
`Literal`	`Term`		A term that directly denotes a datum value. A Literal is a leaf node in the term language — it refers to a concrete Datum via schema:denotes without being a Datum itself.
`Application`	`Term`		A term formed by applying an operation to one or more argument terms. The application's value is the result of evaluating the operator on the evaluated arguments.
`Ring`	`Thing`		The ambient ring Z/(2^n)Z at a specific quantum level n. The Ring is the primary data structure of the UOR kernel. Its two generators (negation and complement) produce the dihedral group D_{2^n} that governs the invariance frame.

Properties

Name	Kind	Functional	Domain	Range	Comment
`value`	Datatype	true	`Datum`	`nonNegativeInteger`	The integer value of a datum element. For a Datum in Z/(2^n)Z, this is an integer in [0, 2^n).
`quantum`	Datatype	true	`Datum`	`positiveInteger`	The quantum level n of a datum, where the datum's ring is Z/(2^n)Z. Determines the bit width and modulus of the datum.
`stratum`	Datatype	true	`Datum`	`nonNegativeInteger`	The ring-layer index of a datum, indicating its position in the stratification of Z/(2^n)Z.
`spectrum`	Datatype	true	`Datum`	`string`	The bit-pattern representation of a datum, encoding its position in the hypercube geometry of Z/(2^n)Z.
`glyph`	Object	true	`Datum`	`Address`	The Braille address associated with this datum, linking the algebraic value to its content-addressable identifier.
`operator`	Object	true	`Application`	`Operation`	The operation applied in an Application term.
`argument`	Object	false	`Application`	`Term`	An argument term in an Application. The ordering of arguments follows rdf:List semantics.
`ringQuantum`	Datatype	true	`Ring`	`positiveInteger`	The bit width n of the ring Z/(2^n)Z. Distinct from schema:quantum on Datum — ringQuantum is the container's bit width; datum quantum is a membership property.
`modulus`	Datatype	true	`Ring`	`positiveInteger`	The modulus 2^n of the ring. Equals 2 raised to the power of ringQuantum.
`generator`	Object	true	`Ring`	`Datum`	The generator element π₁ (value = 1) of the ring. Under iterated successor application, π₁ generates all ring elements.
`negation`	Object	true	`Ring`	`Involution`	The ring reflection involution: neg(x) = (-x) mod 2^n. One of the two generators of the dihedral group D_{2^n}.
`complement`	Object	true	`Ring`	`Involution`	The hypercube reflection involution: bnot(x) = (2^n - 1) ⊕ x. The second generator of the dihedral group D_{2^n}.
`denotes`	Object	true	`Literal`	`Datum`	The datum value that a Literal term denotes. Bridges the Term/Datum disjointness: a Literal refers to a Datum without being one. Evaluation of a Literal produces its denoted Datum.

Named Individuals

Name	Type	Comment
`π₁`	`Datum`	The unique generator of R_n under successor. Value = 1 at every quantum level. Under iterated application of succ, π₁ generates every element of the ring.
`value`: 1
`zero`	`Datum`	The additive identity of the ring. Value = 0 at every quantum level. op:add(x, zero) = x for all x in R_n.
`value`: 0