Observables
Definition
An observable is a measurable quantity computed by the UOR kernel. The class Observable is the root of a taxonomy that classifies measurements by what geometric aspect they capture.
Observable Taxonomy
The observable hierarchy is organized into six categories:
| Class | Description |
|---|---|
| StratumObservable | Layer position within the ring |
| MetricObservable | Geometric distance under a specific metric |
| PathObservable | Properties of paths through the ring |
| ReductionObservable | Operation sequence measurements |
| CatastropheObservable | Qualitative partition changes |
| CurvatureObservable | Gap between ring and Hamming isometry |
Tri-Metric Classification
The three metric observables correspond to the three axes of UOR geometry:
| Metric | Axis | Description |
|---|---|---|
| RingMetric | verticalAxis | d_R(x, y) = |x - y| mod 2^n |
| HammingMetric | horizontalAxis | Number of differing bit positions |
| IncompatibilityMetric | diagonalAxis | Divergence between ring and Hamming distances |
The CurvatureObservable measures the gap between ring-isometry and Hamming-isometry for a given transform. Its subclasses include Commutator and CurvatureFlux.
Measurement Properties
All observables share a common measurement interface:
| Property | Range | Description |
|---|---|---|
| value | xsd:decimal | Numeric measurement value |
| hasUnit | xsd:string | Unit of measurement |
| source | owl:Thing | Source object of the measurement |
| target | owl:Thing | Target object (for pairwise metrics) |
Holonomy Observables
The HolonomyObservable category measures path-dependent transformations:
| Class | Description |
|---|---|
| Monodromy | Net transformation from traversing a loop |
| ParallelTransport | Canonical lift to the tangent bundle |
| DihedralElement | Element of D_{2^n} acting on type space |
Role in Resolution
Observables are consumed by the resolution pipeline. The RefinementSuggestion uses metric axis information (suggestedAxis) to guide which constraints to apply next, informed by observable measurements.
The Jacobian is a curvature observable that decomposes the incompatibility metric site by site — see Differential Calculus for the Jacobian's definition and its role in curvature-weighted constraint selection (DC_10).