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

Classes

NameSubclass OfDisjoint WithComment
ObservableThingA measurable quantity in the UOR Framework. All observables are kernel-computed and user-consumed.
StratumObservableObservableAn observable measuring stratum-level properties: position within the ring's layer structure.
MetricObservableObservableAn observable measuring geometric distance between ring elements under a specific metric.
PathObservableObservableAn observable measuring properties of paths through the ring: path length, total variation, winding number.
CascadeObservableObservableAn observable measuring cascade properties: the length and count of operation sequences.
CatastropheObservableObservableAn observable measuring catastrophe-theoretic properties: thresholds at which qualitative changes occur in the partition.
CurvatureObservableObservableAn observable measuring the curvature of the UOR geometry: the gap between ring-isometry and Hamming-isometry for a given transform.
HolonomyObservableObservableAn observable measuring holonomy: the accumulated transformation when traversing a closed path in the ring.
RingMetricMetricObservableDistance between two ring elements under the ring metric: d_R(x, y) = |x - y| mod 2^n.
HammingMetricMetricObservableDistance between two ring elements under the Hamming metric: the number of bit positions where they differ.
IncompatibilityMetricMetricObservableThe metric incompatibility between two ring elements: the divergence between their ring-metric and Hamming-metric distances, measuring geometric curvature.
StratumValueStratumObservableThe stratum index of a ring element.
StratumDeltaStratumObservableThe difference in stratum between two ring elements.
StratumTrajectoryStratumObservableThe sequence of strata traversed by a path through the ring.
PathLengthPathObservableThe length of a path through the ring, measured in operation steps.
TotalVariationPathObservableThe total variation of a path: the sum of metric distances between consecutive elements.
WindingNumberPathObservableThe winding number of a closed path: the number of times the path wraps around the ring.
CascadeLengthCascadeObservableThe number of operation applications in an operation cascade.
CascadeCountCascadeObservableThe number of distinct cascades in a computation.
CatastropheThresholdCatastropheObservableA critical value at which a qualitative change occurs in the partition structure.
CatastropheCountCatastropheObservableThe number of catastrophe events (qualitative partition changes) in a computation.
CommutatorCurvatureObservableThe commutator [f, g](x) = f(g(x)) - g(f(x)) of two operations, measuring their non-commutativity.
CurvatureFluxCurvatureObservableThe integrated curvature over a region of type space: the total metric incompatibility accumulated.
MonodromyHolonomyObservableThe monodromy of a closed path: the net transformation accumulated when traversing a loop in the type space.
ParallelTransportHolonomyObservableThe parallel transport of a vector along a path: the canonical lift of the path to the tangent bundle of the ring.
DihedralElementHolonomyObservableAn element of the dihedral group D_{2^n} acting on the type space. Each dihedral element induces an isometry of 𝒯_n.

Properties

NameKindFunctionalDomainRangeComment
valueDatatypetrueObservabledecimalThe numeric value of an observable measurement.
unitDatatypetrueObservablestringThe unit of measurement for this observable (e.g., 'bits', 'ring_steps', 'dimensionless').
sourceObjecttrueObservableThingThe source object of this measurement (datum, partition, or path start point).
targetObjecttrueObservableThingThe target object of this measurement (for metrics and path-end measurements).