Resolution & Queries
Resolution is the core operation of the PRISM pipeline's Resolve stage. A Query specifies what to resolve; a Resolver computes the answer by factorizing the input under the dihedral group D_{2^n}.
The Query-Resolver Pattern
The resolution process follows a structured pattern:
- A query specifies the question: what coordinates does this element have? What is its canonical representation? What metrics apply?
- A resolver takes the query and the input element, then computes the answer using ring arithmetic and dihedral group factorization.
- A refinement suggestion is produced if the input is only partially constrained, guiding the next iteration toward a complete resolution.
The Query class in the UOR Queries namespace defines the query interface. The Resolver class in the UOR Resolvers namespace defines the resolver interface.
Iterative Resolution
Not all inputs are fully constrained. When the Site Bundle Semantics budget is not yet closed (some sites remain unpinned), the resolver cannot produce a complete answer in one step. Instead, it enters an iterative loop:
- Attempt resolution with current constraints.
- If incomplete, produce a RefinementSuggestion identifying which additional constraints would help.
- Apply the refinement (pin more sites) and retry.
The CompletenessResolver manages this loop, tracking which constraints have been satisfied and which remain open.
The Constraint Nerve
When constraints interact in complex ways, the CechNerve provides a topological view of the constraint space. It is a simplicial complex whose simplices represent compatible subsets of constraints. The topology of this nerve reveals whether resolution will converge -- see Homological Analysis for the algebraic topology analysis.
Specialized Resolvers
The UOR Resolvers namespace includes several specialized resolvers:
- WittLevelResolver -- resolves which Witt Levels an identity holds at.
- TypeSynthesisResolver -- inverts the resolution pipeline, computing what type is needed given a constraint.
- SessionResolver -- resolves within a session scope, accumulating bindings across steps.
- GeodesicValidator -- verifies that a computation follows the shortest path in the derivation space.
- MeasurementResolver -- handles quantum measurement events that collapse superposed site states.
Connection to the PRISM Pipeline
Resolution is the heart of the Resolve stage. It takes the definitions from Content Addressing and The Partition Decomposition, applies queries, and produces evidence that flows to the Proofs, Derivations & Traces for certification. Observables & Measurement are measured during resolution, recording the geometric and algebraic properties of each computation step.