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/op/
https://uor.foundation/schema/
https://uor.foundation/partition/
https://uor.foundation/type/

Classes

Name	IRI	Subclass Of	Comment
Observable	`https://uor.foundation/observable/Observable`	`http://www.w3.org/2002/07/owl#Thing`	A measurable quantity in the UOR Framework. All observables are kernel-computed and user-consumed.
StratumObservable	`https://uor.foundation/observable/StratumObservable`	`https://uor.foundation/observable/Observable`	An observable measuring stratum-level properties: position within the ring's layer structure.
MetricObservable	`https://uor.foundation/observable/MetricObservable`	`https://uor.foundation/observable/Observable`	An observable measuring geometric distance between ring elements under a specific metric.
PathObservable	`https://uor.foundation/observable/PathObservable`	`https://uor.foundation/observable/Observable`	An observable measuring properties of paths through the ring: path length, total variation, winding number.
ReductionObservable	`https://uor.foundation/observable/ReductionObservable`	`https://uor.foundation/observable/Observable`	An observable measuring reduction properties: the length and count of operation sequences.
CatastropheObservable	`https://uor.foundation/observable/CatastropheObservable`	`https://uor.foundation/observable/Observable`	An observable measuring catastrophe-theoretic properties: thresholds at which qualitative changes occur in the partition.
CurvatureObservable	`https://uor.foundation/observable/CurvatureObservable`	`https://uor.foundation/observable/Observable`	An observable measuring the curvature of the UOR geometry: the gap between ring-isometry and Hamming-isometry for a given transform.
HolonomyObservable	`https://uor.foundation/observable/HolonomyObservable`	`https://uor.foundation/observable/Observable`	An observable measuring holonomy: the accumulated transformation when traversing a closed path in the ring.
SpectralObservable	`https://uor.foundation/observable/SpectralObservable`	`https://uor.foundation/observable/Observable`	ADR-049: an observable whose value is a structural reading of a digest's frequency-domain spectrum. Distinct from the seven internally-derived Observable categories (Stratum / Metric / Path / Reduction / Catastrophe / Curvature / Holonomy) — its values are Walsh–Hadamard parities at specific frequencies, not derivable from the framework's internal algebraic/topological structure. Foundation's typed observable `WalshHadamardParity` per ADR-049 falls under this subclass; predicates over its values enter the typed-commitment surface per ADR-048 as `SingletonCommitment<WalshHadamardParity>` operands.
ValueThresholdObservable	`https://uor.foundation/observable/ValueThresholdObservable`	`https://uor.foundation/observable/Observable`	ADR-040 + ADR-049: an observable whose value is a byte-sequence threshold comparison reading of a digest. Distinct from the seven internally-derived Observable categories (Stratum / Metric / Path / Reduction / Catastrophe / Curvature / Holonomy) and from SpectralObservable / AxisProjectionObservable — its values carry from `(digest as big-endian unsigned integer) <= (target as big-endian unsigned integer)`, the predicate form ADR-040 named when it committed `type:LexicographicLessEqBound`. Foundation's typed observable `LexicographicLessEqThreshold` per ADR-049 falls under this subclass; the canonical search-cost commitment alias `TargetCommitment = SingletonCommitment<LexicographicLessEqThreshold>` per ADR-048 consumes it. The ConstraintRef::Bound.args_repr canonical-string-form encoding for ValueThresholdObservable arguments carries the target byte sequence as the bound's argument directly.
AxisProjectionObservable	`https://uor.foundation/observable/AxisProjectionObservable`	`https://uor.foundation/observable/Observable`	ADR-038: an observable whose value is the axis-realized projection of typed sites through an application-declared AxisTuple kernel per ADR-030. Distinct from the seven internally-derived Observable categories (Stratum, Metric, Path, Reduction, Catastrophe, Curvature, Holonomy) — its values carry from the substrate-extension surface (axis kernels), not from the framework's internal algebraic / topological structure. The closed-catalog discipline holds: foundation owns the subclass; applications consume catalog variants through canonical-string-form `args_repr` on `ConstraintRef::Bound`. The args_repr encoding (per ADR-038) is `axis_address=<hex>;kernel=<symbolic>;sites=<site-list>[;target=<target-spec>]` — axis identification by content-address (AXIS_ADDRESS per ADR-030), not by tuple position, so the encoding is application-invariant.
RingMetric	`https://uor.foundation/observable/RingMetric`	`https://uor.foundation/observable/MetricObservable`	Distance between two ring elements under the ring metric: d_R(x, y) = \|x - y\| mod 2^n.
HammingMetric	`https://uor.foundation/observable/HammingMetric`	`https://uor.foundation/observable/MetricObservable`	Distance between two ring elements under the Hamming metric: the number of bit positions where they differ.
IncompatibilityMetric	`https://uor.foundation/observable/IncompatibilityMetric`	`https://uor.foundation/observable/MetricObservable`	The metric incompatibility between two ring elements: the divergence between their ring-metric and Hamming-metric distances, measuring geometric curvature.
ValueModObservable	`https://uor.foundation/observable/ValueModObservable`	`https://uor.foundation/observable/MetricObservable`	Observes a Datum's value modulo a configurable modulus. Used as the bound observable for BoundConstraint instances representing residue and affine constraint kinds (residueConstraintKind, affineConstraintKind).
GroundingSigma	`https://uor.foundation/observable/GroundingSigma`	`https://uor.foundation/observable/Observable`	Observes the grounding completion ratio σ ∈ [0, 1] of a context, where σ = 1 indicates the ground state (state:GroundedContext). Backs the sigma_metric BaseMetric accessor on Grounded<T>.
JacobianObservable	`https://uor.foundation/observable/JacobianObservable`	`https://uor.foundation/observable/Observable`	Observes the per-site Jacobian row of a Datum at a particular WittLevel, computed as the sequence of partial derivatives of the ring operation with respect to each site coordinate. Backs the jacobian_metric BaseMetric accessor on Grounded<T>; the Rust-side JacobianMetric<L> is parametric over the level marker.
StratumValue	`https://uor.foundation/observable/StratumValue`	`https://uor.foundation/observable/StratumObservable`	The stratum index of a ring element.
StratumDelta	`https://uor.foundation/observable/StratumDelta`	`https://uor.foundation/observable/StratumObservable`	The difference in stratum between two ring elements.
StratumTrajectory	`https://uor.foundation/observable/StratumTrajectory`	`https://uor.foundation/observable/StratumObservable`	The sequence of strata traversed by a path through the ring.
PathLength	`https://uor.foundation/observable/PathLength`	`https://uor.foundation/observable/PathObservable`	The length of a path through the ring, measured in operation steps.
TotalVariation	`https://uor.foundation/observable/TotalVariation`	`https://uor.foundation/observable/PathObservable`	The total variation of a path: the sum of metric distances between consecutive elements.
WindingNumber	`https://uor.foundation/observable/WindingNumber`	`https://uor.foundation/observable/PathObservable`	The winding number of a closed path: the number of times the path wraps around the ring.
ReductionLength	`https://uor.foundation/observable/ReductionLength`	`https://uor.foundation/observable/ReductionObservable`	The number of operation applications in a reduction sequence.
ReductionCount	`https://uor.foundation/observable/ReductionCount`	`https://uor.foundation/observable/ReductionObservable`	The number of distinct reduction sequences in a computation.
CatastropheThreshold	`https://uor.foundation/observable/CatastropheThreshold`	`https://uor.foundation/observable/CatastropheObservable`	A critical value at which a qualitative change occurs in the partition structure.
CatastropheCount	`https://uor.foundation/observable/CatastropheCount`	`https://uor.foundation/observable/CatastropheObservable`	The number of catastrophe events (qualitative partition changes) in a computation.
Commutator	`https://uor.foundation/observable/Commutator`	`https://uor.foundation/observable/CurvatureObservable`	The commutator [f, g](x) = f(g(x)) - g(f(x)) of two operations, measuring their non-commutativity.
CurvatureFlux	`https://uor.foundation/observable/CurvatureFlux`	`https://uor.foundation/observable/CurvatureObservable`	The integrated curvature over a region of type space: the total metric incompatibility accumulated.
Monodromy	`https://uor.foundation/observable/Monodromy`	`https://uor.foundation/observable/HolonomyObservable`	The monodromy of a closed path: the net transformation accumulated when traversing a loop in the type space.
ParallelTransport	`https://uor.foundation/observable/ParallelTransport`	`https://uor.foundation/observable/HolonomyObservable`	The parallel transport of a vector along a path: the canonical lift of the path to the tangent bundle of the ring.
DihedralElement	`https://uor.foundation/observable/DihedralElement`	`https://uor.foundation/observable/HolonomyObservable`	An element of the dihedral group D_{2^n} acting on the type space. Each dihedral element induces an isometry of 𝒯_n.
MeasurementUnit	`https://uor.foundation/observable/MeasurementUnit`	`http://www.w3.org/2002/07/owl#Thing`	A unit of measurement for observable quantities. Each MeasurementUnit individual names a specific unit (bits, ring steps, dimensionless) replacing the string-valued observable:unit property.
Jacobian	`https://uor.foundation/observable/Jacobian`	`https://uor.foundation/observable/CurvatureObservable`	Site-by-site curvature decomposition. J_k measures the discrete derivative of the incompatibility metric at site position k: J_k = \|d_R(x, succ(x)) - d_H(x, succ(x))\| restricted to position k.
TopologicalObservable	`https://uor.foundation/observable/TopologicalObservable`	`https://uor.foundation/observable/Observable`	An observable measuring a topological invariant of the resolution space. Topological observables are invariant under continuous deformations of the constraint configuration.
BettiNumber	`https://uor.foundation/observable/BettiNumber`	`https://uor.foundation/observable/TopologicalObservable`	The rank of a homology group of the constraint nerve. β_k = rank(H_k(N(C))) counts the k-dimensional holes in the constraint configuration.
SpectralGap	`https://uor.foundation/observable/SpectralGap`	`https://uor.foundation/observable/TopologicalObservable`	The smallest positive eigenvalue of the constraint nerve Laplacian. Controls the convergence rate of iterative resolution: larger gap = faster convergence.
ThermoObservable	`https://uor.foundation/observable/ThermoObservable`	`https://uor.foundation/observable/Observable`	An observable measuring thermodynamic properties of the resolution process: residual entropy, Landauer cost, and reduction distribution statistics.
ResidualEntropy	`https://uor.foundation/observable/ResidualEntropy`	`https://uor.foundation/observable/ThermoObservable`	S_residual: the residual Shannon entropy of the site distribution after partial resolution. Computed as S = (Σ κ_k − χ(N(C))) × ln 2 (IT_7b). Unit: Nats.
LandauerCost	`https://uor.foundation/observable/LandauerCost`	`https://uor.foundation/observable/ThermoObservable`	The minimum thermodynamic cost (in units of k_B T ln 2) of erasing one bit of site uncertainty. The UOR ring operates at β* = ln 2 — the Landauer temperature.
LandauerBudget	`https://uor.foundation/observable/LandauerBudget`	`https://uor.foundation/observable/ThermoObservable`	A sealed observable carrier for accumulated Landauer cost in nats. Monotonic within a single pipeline invocation. The UOR ring operates at the Landauer temperature (β* = ln 2), so this observable is a direct measure of irreversible bit-erasure performed by the computation up to the witness it accompanies.
ReductionEntropy	`https://uor.foundation/observable/ReductionEntropy`	`https://uor.foundation/observable/ThermoObservable`	The Shannon entropy of the reduction distribution P(j) = 2^{−j}. At the Landauer temperature, this equals ln 2 per reduction step — each step erases exactly one bit of site uncertainty.
SynthesisSignature	`https://uor.foundation/observable/SynthesisSignature`	`http://www.w3.org/2002/07/owl#Thing`	A named topological signature: a pair (realised Euler characteristic, realised Betti profile). Linked from TypeSynthesisResult. Allows comparison between the goal signature and the actually achieved signature.
SpectralSequencePage	`https://uor.foundation/observable/SpectralSequencePage`	`http://www.w3.org/2002/07/owl#Thing`	A single page E_r of the quantum level spectral sequence. Carries the page index r and the differential d_r. The sequence converges when all differentials vanish — typically by E_3 for simple constraint configurations.
LiftObstructionClass	`https://uor.foundation/observable/LiftObstructionClass`	`http://www.w3.org/2002/07/owl#Thing`	The cohomology class in H^2(N(C(T))) representing the LiftObstruction for a specific WittLift. The class is zero iff the obstruction is trivial. When non-zero, it indexes the specific site pair at Q_{n+1} that cannot be closed by the lifted constraint set alone.
MonodromyClass	`https://uor.foundation/observable/MonodromyClass`	`http://www.w3.org/2002/07/owl#Thing`	A classification of a type's holonomy: the subgroup of D_{2^n} generated by all Monodromy observables computed over closed paths in the type's constraint nerve. Trivial iff every closed constraint path returns to its starting site assignment without net dihedral transformation.
HolonomyGroup	`https://uor.foundation/observable/HolonomyGroup`	`http://www.w3.org/2002/07/owl#Thing`	The holonomy group of a ConstrainedType: the group of all Monodromy elements achievable by closed paths in the constraint nerve. Always a subgroup of D_{2^n}. Trivial iff the type has trivial monodromy everywhere; equals D_{2^n} iff paths involving both neg and bnot involutions are present.
ClosedConstraintPath	`https://uor.foundation/observable/ClosedConstraintPath`	`http://www.w3.org/2002/07/owl#Thing`	A sequence of constraint applications forming a closed loop in the constraint nerve — beginning and ending at the same site assignment. The Monodromy of the loop is the net DihedralElement accumulated when traversing it.
PhaseBoundaryType	`https://uor.foundation/observable/PhaseBoundaryType`	`http://www.w3.org/2002/07/owl#Thing`	A classification of phase boundary in the catastrophe diagram: period boundary (g divides 2^n − 1) or power-of-two boundary (g = 2^k).
AchievabilityStatus	`https://uor.foundation/observable/AchievabilityStatus`	`http://www.w3.org/2002/07/owl#Thing`	The achievability classification of a topological signature in the morphospace. Either Achievable or Forbidden (witnessed by ImpossibilityWitness).
HomotopyGroup	`https://uor.foundation/observable/HomotopyGroup`	`http://www.w3.org/2002/07/owl#Thing`	The k-th homotopy group πk(N(C), v) of the constraint nerve based at vertex v.
HigherMonodromy	`https://uor.foundation/observable/HigherMonodromy`	`http://www.w3.org/2002/07/owl#Thing`	The image of πk(N(C)) → Aut(sitek) for k > 1. Generalises the MN_6 monodromy homomorphism.
WhiteheadProduct	`https://uor.foundation/observable/WhiteheadProduct`	`http://www.w3.org/2002/07/owl#Thing`	The Whitehead product [α, β] ∈ πp+q−1 for α ∈ πp, β ∈ πq.
StratificationRecord	`https://uor.foundation/observable/StratificationRecord`	`http://www.w3.org/2002/07/owl#Thing`	A record of the holonomy stratification of the moduli space at a given quantum level: the list of HolonomyStrata, their codimensions, and their relationship to the MorphospaceBoundary.
BaseMetric	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/observable/Observable`	Superclass for the six universal measurements. Every computation on the ring produces these six quantities: d_Δ, σ, J_k, β_k, χ, r.
GroundingObservable	`https://uor.foundation/observable/GroundingObservable`	`https://uor.foundation/observable/Observable`	The grounding metric σ = pinned sites / total sites. Ranges from 0 (no sites pinned) to 1 (fully grounded).
EulerCharacteristicObservable	`https://uor.foundation/observable/EulerCharacteristicObservable`	`https://uor.foundation/observable/Observable`	The Euler characteristic χ = Σ(−1)^k β_k of the constraint nerve. An integer-valued topological invariant.

Properties

Name	Kind	Functional	Domain	Range	Comment
value	Datatype	true	`https://uor.foundation/observable/Observable`	`http://www.w3.org/2001/XMLSchema#decimal`	The numeric value of an observable measurement.
source	Object	true	`https://uor.foundation/observable/Observable`	`http://www.w3.org/2002/07/owl#Thing`	The source object of this measurement (datum, partition, or path start point).
target	Object	true	`https://uor.foundation/observable/Observable`	`http://www.w3.org/2002/07/owl#Thing`	The target object of this measurement (for metrics and path-end measurements).
hasUnit	Object	true	`https://uor.foundation/observable/Observable`	`https://uor.foundation/observable/MeasurementUnit`	The measurement unit of this observable. Replaces the string-valued observable:unit property with a typed reference to a MeasurementUnit individual.
sitePosition	Datatype	true	`https://uor.foundation/observable/Jacobian`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The site position k at which this Jacobian entry is measured.
derivativeValue	Datatype	true	`https://uor.foundation/observable/Jacobian`	`http://www.w3.org/2001/XMLSchema#decimal`	The discrete derivative value at this site position.
dimension	Datatype	true	`https://uor.foundation/observable/TopologicalObservable`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension k of the topological observable (e.g., the degree of the Betti number or the dimension of the spectral gap).
realisedEuler	Datatype	true	`https://uor.foundation/observable/SynthesisSignature`	`http://www.w3.org/2001/XMLSchema#integer`	The Euler characteristic actually achieved by this synthesis signature.
realisedBetti	Datatype	false	`https://uor.foundation/observable/SynthesisSignature`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Non-functional. Realised Betti number values, one assertion per homological degree.
pageIndex	Datatype	true	`https://uor.foundation/observable/SpectralSequencePage`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The page r of this spectral sequence page. r=1 is the initial page; convergence is declared when all d_r are zero.
differentialIsZero	Datatype	true	`https://uor.foundation/observable/SpectralSequencePage`	`http://www.w3.org/2001/XMLSchema#boolean`	True iff d_r = 0 on this page — no further corrections to the lifted homology.
convergedAt	Datatype	true	`https://uor.foundation/observable/SpectralSequencePage`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The page index r at which the spectral sequence converged (all subsequent differentials zero).
obstructionClass	Object	true	`https://uor.foundation/observable/LiftObstructionClass`	`https://uor.foundation/cohomology/CohomologyGroup`	The cohomology class in H^2(N(C(T))) representing this obstruction.
monodromyLoop	Object	true	`https://uor.foundation/observable/Monodromy`	`https://uor.foundation/observable/ClosedConstraintPath`	The closed path that generates this monodromy value.
monodromyElement	Object	true	`https://uor.foundation/observable/Monodromy`	`https://uor.foundation/observable/DihedralElement`	The dihedral element g in D_{2^n} accumulated when traversing the loop. The monodromy is trivial iff this element is the group identity.
isTrivialMonodromy	Datatype	true	`https://uor.foundation/observable/Monodromy`	`http://www.w3.org/2001/XMLSchema#boolean`	True iff the monodromyElement is the identity in D_{2^n}.
holonomyGroup	Object	false	`https://uor.foundation/observable/HolonomyGroup`	`https://uor.foundation/observable/DihedralElement`	Non-functional. The generators of the holonomy group: one DihedralElement per generating monodromy.
holonomyGroupOrder	Datatype	true	`https://uor.foundation/observable/HolonomyGroup`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The order of the holonomy group as a subgroup of D_{2^n}. For a FlatType: 1. For full dihedral holonomy: 2^{n+1}.
pathLength	Datatype	true	`https://uor.foundation/observable/ClosedConstraintPath`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The number of constraint application steps in this closed path.
pathConstraints	Object	false	`https://uor.foundation/observable/ClosedConstraintPath`	`https://uor.foundation/type/Constraint`	Non-functional. The ordered sequence of constraints traversed. One assertion per step.
dihedralElementValue	Object	false	`https://uor.foundation/observable/DihedralElement`	`https://uor.foundation/op/Operation`	Non-functional. One assertion per generator in the normal form of the element — the sequence of neg and/or bnot operations that realises this dihedral element when composed.
isIdentityElement	Datatype	true	`https://uor.foundation/observable/DihedralElement`	`http://www.w3.org/2001/XMLSchema#boolean`	True iff this element is the group identity (the trivial monodromy value).
elementOrder	Datatype	true	`https://uor.foundation/observable/DihedralElement`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The order of this element in D_{2^n}: the smallest k >= 1 such that g^k = id. For neg and bnot: order 2.
hardnessEstimate	Datatype	true	`https://uor.foundation/observable/ThermoObservable`	`http://www.w3.org/2001/XMLSchema#decimal`	An estimated computational hardness for a ThermoObservable, connecting thermodynamic cost to complexity (TH_9 realisation).
phaseN	Datatype	true	`https://uor.foundation/observable/CatastropheObservable`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The ring dimension coordinate n in the (n, g) catastrophe phase diagram (PD_1 n-coordinate).
phaseG	Datatype	true	`https://uor.foundation/observable/CatastropheObservable`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The group-order coordinate g in the (n, g) catastrophe phase diagram (PD_1 g-coordinate).
onResonanceLine	Datatype	true	`https://uor.foundation/observable/CatastropheObservable`	`http://www.w3.org/2001/XMLSchema#boolean`	True when g divides 2^n − 1, placing this observable on a resonance line in the phase diagram (PD_4).
phaseBoundaryType	Object	true	`https://uor.foundation/observable/CatastropheObservable`	`https://uor.foundation/observable/PhaseBoundaryType`	The type of phase boundary at this point in the catastrophe diagram: PeriodBoundary or PowerOfTwoBoundary (PD_2).
achievabilityStatus	Object	true	`https://uor.foundation/observable/SynthesisSignature`	`https://uor.foundation/observable/AchievabilityStatus`	The achievability classification of this observable's topological signature in the morphospace.
isAchievable	Datatype	true	`https://uor.foundation/observable/SynthesisSignature`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this signature has been empirically verified as achievable at some quantum level.
isForbidden	Datatype	true	`https://uor.foundation/observable/SynthesisSignature`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this signature has been formally proven impossible by an ImpossibilityWitness.
achievabilityWitness	Object	true	`https://uor.foundation/observable/SynthesisSignature`	`https://uor.foundation/proof/Proof`	The proof individual (ImpossibilityWitness or AxiomaticDerivation) that grounds this signature's achievability classification.
rotationExponent	Datatype	true	`https://uor.foundation/observable/DihedralElement`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The rotation exponent k ∈ \[0, 2^n) of this dihedral element in the standard representation r^k s^s. Together with reflectionBit, uniquely identifies the element within D_\{2^n\}.
reflectionBit	Datatype	true	`https://uor.foundation/observable/DihedralElement`	`http://www.w3.org/2001/XMLSchema#boolean`	The reflection flag s ∈ \{0,1\} of this dihedral element. False = pure rotation (r^k), true = reflection (r^k·s). D_7 defines composition: (r^a s^p)(r^b s^q) = r^(a + (-1)^p b) s^(p XOR q).
homotopyDimension	Datatype	true	`https://uor.foundation/observable/HomotopyGroup`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension k of this homotopy group πk.
homotopyRank	Datatype	true	`https://uor.foundation/observable/HomotopyGroup`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The rank of this homotopy group (number of free generators).
homotopyBasepoint	Object	true	`https://uor.foundation/observable/HomotopyGroup`	`https://uor.foundation/type/Constraint`	The basepoint vertex v at which this homotopy group is computed.
higherMonodromyDimension	Datatype	true	`https://uor.foundation/observable/HigherMonodromy`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The dimension k > 1 at which this higher monodromy acts.
whiteheadTrivial	Datatype	true	`https://uor.foundation/observable/WhiteheadProduct`	`http://www.w3.org/2001/XMLSchema#boolean`	True iff this Whitehead product is trivial (zero in πp+q−1).
postnikovTruncation	Object	true	`https://uor.foundation/observable/SpectralSequencePage`	`https://uor.foundation/homology/PostnikovTruncation`	The Postnikov truncation associated with this spectral sequence page.
stratificationLevel	Object	true	`https://uor.foundation/observable/StratificationRecord`	`https://uor.foundation/schema/WittLevel`	The quantum level at which this stratification is computed.
stratificationStratum	Object	false	`https://uor.foundation/observable/StratificationRecord`	`https://uor.foundation/type/HolonomyStratum`	A HolonomyStratum in this stratification record.
metricDomain	Datatype	true	`https://uor.foundation/observable/BaseMetric`	`http://www.w3.org/2001/XMLSchema#string`	The mathematical domain of this base metric.
metricRange	Datatype	true	`https://uor.foundation/observable/BaseMetric`	`http://www.w3.org/2001/XMLSchema#string`	The mathematical range (codomain) of this base metric.
metricComposition	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/schema/TermExpression`	How this metric composes with others in the measurement tower.
referencesClass	Annotation	true	`https://uor.foundation/observable/BaseMetric`	`http://www.w3.org/2001/XMLSchema#string`	IRI of the existing observable class that this base metric references. Annotation-valued (not ObjectProperty) because the assertion is a class-level reference, not an instance-level one: the metric describes a class of Observable phenomena, not a specific individual.
referencesIdentity	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/op/Identity`	The existing identity that defines this base metric.
saturationNumerator	Datatype	true	`https://uor.foundation/observable/GroundingObservable`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The count of pinned sites (numerator of σ).
saturationDenominator	Datatype	true	`https://uor.foundation/observable/GroundingObservable`	`http://www.w3.org/2001/XMLSchema#positiveInteger`	The total site count (denominator of σ).
alternatingSum	Object	true	`https://uor.foundation/observable/EulerCharacteristicObservable`	`https://uor.foundation/schema/TermExpression`	The alternating sum formula for Euler characteristic.
metricUnit	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/observable/MeasurementUnit`	The unit of measurement for this base metric.
metricPrecision	Datatype	true	`https://uor.foundation/observable/BaseMetric`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The precision or resolution of this base metric.
metricMonotonicity	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/schema/TermExpression`	Monotonicity property of this metric (e.g., non-decreasing).
metricDecomposition	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/schema/TermExpression`	The decomposition rule for this metric into sub-metrics.
metricTowerPosition	Datatype	true	`https://uor.foundation/observable/BaseMetric`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The position of this metric in the metric tower.
metricComputationCost	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/schema/TermExpression`	The computational cost of evaluating this metric.
metricBound	Object	true	`https://uor.foundation/observable/BaseMetric`	`https://uor.foundation/schema/TermExpression`	Upper or lower bound on the metric value.
landauerNats	Datatype	true	`https://uor.foundation/observable/LandauerBudget`	`http://www.w3.org/2001/XMLSchema#decimal`	The accumulated Landauer cost carried by a LandauerBudget instance, measured in nats. Monotonic within a pipeline invocation. The unit is observable:Nats — every increment corresponds to a number of irreversible bit-erasures times ln 2 (op:OA_5).

Named Individuals

Name	Type	Properties	Comment
Bits	`https://uor.foundation/observable/MeasurementUnit`	—	Information-theoretic unit: the measurement is in bits (e.g., Hamming weight, entropy).
RingSteps	`https://uor.foundation/observable/MeasurementUnit`	—	Ring-arithmetic unit: the measurement is in ring distance steps (\|x - y\| mod 2^n).
Dimensionless	`https://uor.foundation/observable/MeasurementUnit`	—	Dimensionless unit: the measurement is a pure number (e.g., winding number, Betti number, spectral gap).
Nats	`https://uor.foundation/observable/MeasurementUnit`	—	Natural information unit: entropy measured in nats (using natural logarithm). S_residual is expressed in nats when computed as (Σ κ_k − χ) × ln 2.
PeriodBoundary	`https://uor.foundation/observable/PhaseBoundaryType`	—	A phase boundary where g divides 2^n − 1, meaning g is a period of the multiplicative structure of R_n.
PowerOfTwoBoundary	`https://uor.foundation/observable/PhaseBoundaryType`	—	A phase boundary where g = 2^k, meaning g aligns with the binary stratification of R_n.
Achievable	`https://uor.foundation/observable/AchievabilityStatus`	—	The signature has been verified as achievable at some quantum level by an AxiomaticDerivation proof.
Forbidden	`https://uor.foundation/observable/AchievabilityStatus`	—	The signature has been formally proven impossible by an ImpossibilityWitness deriving from MS_1, MS_2, or other impossibility theorems.
d_delta_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: pair of ring elements `metricRange`: non-negative integer `referencesClass`: `https://uor.foundation/observable/IncompatibilityMetric`	d_Δ: the incompatibility metric \|d_R − d_H\| per site pair.
sigma_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: computation state `metricRange`: decimal in [0, 1] `referencesIdentity`: `https://uor.foundation/op/GS_2`	σ: the grounding metric, pinned sites / total sites.
jacobian_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: computation state × site index `metricRange`: decimal `referencesClass`: `https://uor.foundation/observable/Jacobian` `referencesIdentity`: `https://uor.foundation/op/DC_6`	J_k: per-site curvature, ∂_R f_k.
betti_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: simplicial complex × dimension `metricRange`: non-negative integer `referencesClass`: `https://uor.foundation/observable/BettiNumber`	β_k: per-dimension Betti number of the constraint nerve.
euler_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: simplicial complex `metricRange`: integer `referencesIdentity`: `https://uor.foundation/op/IT_2`	χ: Euler characteristic, Σ(−1)^k β_k.
residual_metric	`https://uor.foundation/observable/BaseMetric`	`metricDomain`: computation state `metricRange`: non-negative integer `referencesClass`: `https://uor.foundation/observable/ResidualEntropy`	r: count of free (unpinned) sites, the residual entropy.