Explore the Ontology
The UOR Foundation ontology comprises 33 namespaces organized into three space classifications: Kernel (immutable substrate), Bridge (computed transforms), and User (runtime parameterization). The diagram below shows import dependencies.
Each namespace imports other namespaces for its domain and range declarations, forming a directed acyclic graph. The assembly order (u → schema → op → … → state) ensures no circular dependencies. Expand a namespace below for a summary, or visit its full reference page. For a conceptual overview, start with The PRISM Pipeline.
Kernel Space
u — UOR Content Addressing
Content-addressable identifiers for ring elements. Each element carries a unique content-derived identifier.
- Classes
- 1
- Properties
- 6
- Individuals
- 0
schema — UOR Schema
Core value types and term language for the UOR ring substrate. Defines Datum (ring element), Term (syntactic expression), and the Ring container.
- Classes
- 21
- Properties
- 32
- Individuals
- 1878
op — UOR Operations
Ring operations, involutions, algebraic identities, and the dihedral symmetry group D_{2^n} generated by neg and bnot.
- Classes
- 19
- Properties
- 42
- Individuals
- 663
carry — UOR Carry Algebra
Carry chain algebra: generate/propagate/kill event classification, carry profiles, encoding configurations, and encoding quality metrics for d_Δ optimization.
- Classes
- 5
- Properties
- 15
- Individuals
- 0
reduction — UOR Euler Reduction
Sequential composition of ψ-maps into a parameterized reduction ψ = ψ_9 ∘ … ∘ ψ_1. Defines stages, phase gates, rollback, and epochs.
- Classes
- 38
- Properties
- 93
- Individuals
- 44
convergence — UOR Convergence Tower
Hopf convergence tower: four levels R, C, H, O corresponding to the four normed division algebras of dimensions 1, 2, 4, 8. Each level carries a Hopf fibration fiber and Betti signature.
- Classes
- 5
- Properties
- 15
- Individuals
- 8
division — UOR Division Algebras
The four normed division algebras R, C, H, O and the Cayley-Dickson construction.
- Classes
- 5
- Properties
- 9
- Individuals
- 7
monoidal — UOR Monoidal Composition
Sequential composition of computations via monoidal product A ⊗ B.
- Classes
- 3
- Properties
- 8
- Individuals
- 0
operad — UOR Operad Composition
Structural type nesting via operad composition. Governs how types compose: Table(Tuple(Sequence(Symbol(...)))).
- Classes
- 2
- Properties
- 6
- Individuals
- 0
effect — UOR Effect Algebra
Typed endomorphisms on state:Context classified by site target. Formalizes what reduction guard-effect pairs do to the site budget.
- Classes
- 9
- Properties
- 14
- Individuals
- 0
predicate — UOR Predicates and Dispatch
Boolean-valued functions on kernel objects. Formalizes resolver dispatch, reduction guard evaluation, and conditional resolution paths.
- Classes
- 9
- Properties
- 15
- Individuals
- 12
parallel — UOR Parallel Composition
Independent computations over provably disjoint site budgets. Formalizes when execution order is irrelevant.
- Classes
- 5
- Properties
- 10
- Individuals
- 0
stream — UOR Productive Streams
Coinductive sequences of reduction epochs. Each epoch terminates independently; the stream is the unbounded composition of terminating epochs.
- Classes
- 6
- Properties
- 13
- Individuals
- 0
failure — UOR Failure Algebra
Partial computations, typed failure propagation, and recovery. Formalizes how computations that cannot reach convergence are represented, composed, and recovered from within the ring substrate.
- Classes
- 12
- Properties
- 11
- Individuals
- 0
linear — UOR Linear Resources
Linear discipline on site consumption. Formalizes that each site in a complete resolution path is targeted by exactly one effect.
- Classes
- 6
- Properties
- 8
- Individuals
- 0
recursion — UOR Bounded Recursion
Self-referential computations with well-founded descent measures guaranteeing termination.
- Classes
- 7
- Properties
- 10
- Individuals
- 0
region — UOR Address Regions
Spatial locality of content-addressed ring elements. Defines computable working sets for resolver stages, independent of physical memory layout.
- Classes
- 5
- Properties
- 11
- Individuals
- 0
Bridge Space
query — UOR Queries
Information extraction queries. Users initiate queries; the kernel resolves them against the ring substrate.
- Classes
- 7
- Properties
- 10
- Individuals
- 3
resolver — UOR Resolvers
Type resolution strategies implementing the partition map Π : T_n → Part(R_n). Resolvers transform type declarations into ring partitions.
- Classes
- 26
- Properties
- 47
- Individuals
- 8
partition — UOR Partitions
Irreducibility partitions produced by type resolution. A partition divides the ring into four disjoint components: Irreducible, Reducible, Units, and Exterior.
- Classes
- 11
- Properties
- 28
- Individuals
- 0
observable — UOR Observables
Observable quantities and metrics computed by the UOR kernel. Includes ring-metric, Hamming-metric, curvature, holonomy, and catastrophe-theoretic observables.
- Classes
- 50
- Properties
- 57
- Individuals
- 14
homology — UOR Homology
Simplicial complexes, chain complexes, boundary operators, and homology groups for structural reasoning.
- Classes
- 14
- Properties
- 35
- Individuals
- 5
cohomology — UOR Cohomology
Cochain complexes, sheaf cohomology, and local-to-global obstruction detection.
- Classes
- 10
- Properties
- 20
- Individuals
- 4
proof — UOR Proofs
Kernel-produced verification proofs attesting to algebraic properties of UOR objects and operations.
- Classes
- 16
- Properties
- 27
- Individuals
- 656
derivation — UOR Derivations
Computation witnesses recording term rewriting sequences from original terms to their canonical forms.
- Classes
- 8
- Properties
- 22
- Individuals
- 6
trace — UOR Computation Traces
Execution traces recording the sequence of kernel operations, intermediate results, and accumulated metrics for a computation.
- Classes
- 7
- Properties
- 30
- Individuals
- 7
cert — UOR Certificates
Kernel-produced attestation certificates for transforms, isometries, and involutions. Each certificate verifies that a specific structural property holds.
- Classes
- 13
- Properties
- 26
- Individuals
- 0
interaction — UOR Interaction Algebra
Multi-entity interaction: commutator states, associator triples, negotiation convergence.
- Classes
- 9
- Properties
- 25
- Individuals
- 0
boundary — UOR IO Boundary
Typed interface between kernel computation and the external world. Formalizes how data enters and exits the ring substrate.
- Classes
- 8
- Properties
- 12
- Individuals
- 0
conformance — UOR Conformance Shapes
SHACL-equivalent constraint shapes defining what a Prism implementation must provide at each extension point. Machine-verifiable contracts.
- Classes
- 30
- Properties
- 49
- Individuals
- 10
User Space
type — UOR Type System
Runtime type declarations that parameterize the resolution pipeline. Types are declared by Prism applications and resolved to partitions of the ring.
- Classes
- 39
- Properties
- 86
- Individuals
- 17
morphism — UOR Transforms and Morphisms
Runtime abstractions for maps between UOR objects: transforms, isometries, embeddings, and group actions. The foundation provides the vocabulary; Prism writes the sentences.
- Classes
- 20
- Properties
- 56
- Individuals
- 7
state — UOR State
Parameterized address spaces, context management, binding lifecycle, and state transitions. The user-space overlay onto the kernel's read-only ring substrate.
- Classes
- 15
- Properties
- 43
- Individuals
- 7