UOR Observables

IRI
https://uor.foundation/observable/
Prefix
observable:
Space
bridge
Comment
Observable quantities and metrics computed by the UOR kernel. Includes ring-metric, Hamming-metric, curvature, holonomy, and catastrophe-theoretic observables.

Imports

  • https://uor.foundation/schema/
  • https://uor.foundation/partition/

Classes

NameIRISubclass OfDisjoint WithComment
Observablehttps://uor.foundation/observable/Observablehttp://www.w3.org/2002/07/owl#ThingA measurable quantity in the UOR Framework. All observables are kernel-computed and user-consumed.
StratumObservablehttps://uor.foundation/observable/StratumObservablehttps://uor.foundation/observable/ObservableAn observable measuring stratum-level properties: position within the ring's layer structure.
MetricObservablehttps://uor.foundation/observable/MetricObservablehttps://uor.foundation/observable/ObservableAn observable measuring geometric distance between ring elements under a specific metric.
PathObservablehttps://uor.foundation/observable/PathObservablehttps://uor.foundation/observable/ObservableAn observable measuring properties of paths through the ring: path length, total variation, winding number.
CascadeObservablehttps://uor.foundation/observable/CascadeObservablehttps://uor.foundation/observable/ObservableAn observable measuring cascade properties: the length and count of operation sequences.
CatastropheObservablehttps://uor.foundation/observable/CatastropheObservablehttps://uor.foundation/observable/ObservableAn observable measuring catastrophe-theoretic properties: thresholds at which qualitative changes occur in the partition.
CurvatureObservablehttps://uor.foundation/observable/CurvatureObservablehttps://uor.foundation/observable/ObservableAn observable measuring the curvature of the UOR geometry: the gap between ring-isometry and Hamming-isometry for a given transform.
HolonomyObservablehttps://uor.foundation/observable/HolonomyObservablehttps://uor.foundation/observable/ObservableAn observable measuring holonomy: the accumulated transformation when traversing a closed path in the ring.
RingMetrichttps://uor.foundation/observable/RingMetrichttps://uor.foundation/observable/MetricObservableDistance between two ring elements under the ring metric: d_R(x, y) = |x - y| mod 2^n.
HammingMetrichttps://uor.foundation/observable/HammingMetrichttps://uor.foundation/observable/MetricObservableDistance between two ring elements under the Hamming metric: the number of bit positions where they differ.
IncompatibilityMetrichttps://uor.foundation/observable/IncompatibilityMetrichttps://uor.foundation/observable/MetricObservableThe metric incompatibility between two ring elements: the divergence between their ring-metric and Hamming-metric distances, measuring geometric curvature.
StratumValuehttps://uor.foundation/observable/StratumValuehttps://uor.foundation/observable/StratumObservableThe stratum index of a ring element.
StratumDeltahttps://uor.foundation/observable/StratumDeltahttps://uor.foundation/observable/StratumObservableThe difference in stratum between two ring elements.
StratumTrajectoryhttps://uor.foundation/observable/StratumTrajectoryhttps://uor.foundation/observable/StratumObservableThe sequence of strata traversed by a path through the ring.
PathLengthhttps://uor.foundation/observable/PathLengthhttps://uor.foundation/observable/PathObservableThe length of a path through the ring, measured in operation steps.
TotalVariationhttps://uor.foundation/observable/TotalVariationhttps://uor.foundation/observable/PathObservableThe total variation of a path: the sum of metric distances between consecutive elements.
WindingNumberhttps://uor.foundation/observable/WindingNumberhttps://uor.foundation/observable/PathObservableThe winding number of a closed path: the number of times the path wraps around the ring.
CascadeLengthhttps://uor.foundation/observable/CascadeLengthhttps://uor.foundation/observable/CascadeObservableThe number of operation applications in an operation cascade.
CascadeCounthttps://uor.foundation/observable/CascadeCounthttps://uor.foundation/observable/CascadeObservableThe number of distinct cascades in a computation.
CatastropheThresholdhttps://uor.foundation/observable/CatastropheThresholdhttps://uor.foundation/observable/CatastropheObservableA critical value at which a qualitative change occurs in the partition structure.
CatastropheCounthttps://uor.foundation/observable/CatastropheCounthttps://uor.foundation/observable/CatastropheObservableThe number of catastrophe events (qualitative partition changes) in a computation.
Commutatorhttps://uor.foundation/observable/Commutatorhttps://uor.foundation/observable/CurvatureObservableThe commutator [f, g](x) = f(g(x)) - g(f(x)) of two operations, measuring their non-commutativity.
CurvatureFluxhttps://uor.foundation/observable/CurvatureFluxhttps://uor.foundation/observable/CurvatureObservableThe integrated curvature over a region of type space: the total metric incompatibility accumulated.
Monodromyhttps://uor.foundation/observable/Monodromyhttps://uor.foundation/observable/HolonomyObservableThe monodromy of a closed path: the net transformation accumulated when traversing a loop in the type space.
ParallelTransporthttps://uor.foundation/observable/ParallelTransporthttps://uor.foundation/observable/HolonomyObservableThe parallel transport of a vector along a path: the canonical lift of the path to the tangent bundle of the ring.
DihedralElementhttps://uor.foundation/observable/DihedralElementhttps://uor.foundation/observable/HolonomyObservableAn element of the dihedral group D_{2^n} acting on the type space. Each dihedral element induces an isometry of 𝒯_n.

Properties

NameKindFunctionalDomainRangeComment
valueDatatypetruehttps://uor.foundation/observable/Observablehttp://www.w3.org/2001/XMLSchema#decimalThe numeric value of an observable measurement.
unitDatatypetruehttps://uor.foundation/observable/Observablehttp://www.w3.org/2001/XMLSchema#stringThe unit of measurement for this observable (e.g., 'bits', 'ring_steps', 'dimensionless').
sourceObjecttruehttps://uor.foundation/observable/Observablehttp://www.w3.org/2002/07/owl#ThingThe source object of this measurement (datum, partition, or path start point).
targetObjecttruehttps://uor.foundation/observable/Observablehttp://www.w3.org/2002/07/owl#ThingThe target object of this measurement (for metrics and path-end measurements).