Observables & Measurement
The UOR Observables namespace defines what can be measured during resolution. Observables are bridge-space objects that quantify geometric, topological, and algebraic properties of ring elements and their types.
What Is an Observable?
An Observable is a measurable quantity attached to a computation. During Resolution & Queries, the resolver computes not just the answer to a query but also a collection of observable measurements: ring distance, Hamming distance, curvature, spectral data, and more.
These measurements serve two purposes:
- Diagnostic -- they reveal the geometric structure of the computation, helping identify obstructions or convergence properties.
- Evidential -- they provide the quantitative evidence that proofs and certificates reference when attesting to a result.
Metric Axes
The MetricAxis enum class defines the
named measurement dimensions. Each axis represents a different way of measuring
distance or similarity in the ring:
- Ring distance (arithmetic difference modulo 2^n)
- Hamming distance (bitwise difference count)
- Curvature (local geometric bending)
These axes parameterize the multi-metric structure of UOR -- the same pair of elements can have different distances depending on which metric axis is used.
Holonomy and Monodromy
When a Site Bundle Semantics is transported around a loop in the base space, it may return to a different state. This transformation is the holonomy.
The HolonomyGroup captures the group of all holonomy transformations at a base point. The Monodromy class records the representation of the fundamental group in the holonomy group.
If all holonomies are trivial, the bundle is flat. Otherwise, it is twisted --
a distinction formalized by type:FlatType and type:TwistedType in the
UOR Type System namespace.
Measurement and State Collapse
The MeasurementEvent class records when an observable is measured during resolution. For superposed site states (where a site is a quantum superposition of types), measurement collapses the superposition into a definite type.
The AchievabilityStatus enum classifies targets as either Achievable or Forbidden -- determining whether a morphospace target is reachable from the current state.
Connection to the PRISM Pipeline
Observables are computed during the Resolve stage by the Resolution & Queries machinery. They produce the quantitative evidence that feeds into the Proofs, Derivations & Traces certification pathway. The topological observables (holonomy, monodromy, spectral sequences) connect directly to the Homological Analysis layer that diagnoses convergence obstructions.
See also Witt Levels for how observables are scoped to specific ring scales.