UOR Framework Overview

The Universal Object Reference (UOR) Framework is a formal ontology and mathematical framework for content-addressed object spaces. It provides a unified model for representing, resolving, and transforming any computable object using an algebraic substrate based on ring theory and group symmetry.

Core Ideas

Content addressing means an object is identified by what it is, not where it is. The UOR framework formalizes this via Address: every object has a canonical address derived from its content, not from an external naming system.

The ring substrate Ring is the algebraic foundation: Z/(2^n)Z — integers modulo 2^n. At quantum level n=8 this is the byte ring (Z/256Z), familiar from computer arithmetic.

Two involutions generate the structure:

• neg: ring negation (reflection)
• bnot: bitwise complement (hypercube reflection)

These generate the dihedral group D_{2^n}, captured by DihedralGroup.

The critical identity Critical Identity: neg(bnot(x)) = succ(x) for all x ∈ R_n — successor is the composition of the two involutions. This is the foundational theorem proved by CriticalIdentityProof.

Namespace Layers

The 14 namespaces are organized into three space classifications:

Kernel (mathematical core):

• Address — universal addressing
• Ring — ring substrate
• Operation — operations

Bridge (resolution infrastructure):

• Query — queries
• Resolver — resolvers
• Partition — partitions
• Observable — observables
• Proof — proofs
• Derivation — derivations
• ComputationTrace — traces
• Certificate — certificates

User (application layer):

• TypeDefinition — types
• Transform — morphisms
• Context — state

How It Works

1. A value has a type (TypeDefinition)
2. A query (Query) asks about the value
3. A resolver (Resolver) factorizes it in the ring
4. The partition (Partition) decomposes the result
5. Observables (Observable) measure properties
6. A certificate (Certificate) attests correctness
7. A trace (ComputationTrace) records the computation
8. State (Context) maintains evaluation context