UOR Computation Traces

IRI: https://uor.foundation/trace/
Prefix: trace:
Space: bridge
Comment: Execution traces recording the sequence of kernel operations, intermediate results, and accumulated metrics for a computation.

Imports

https://uor.foundation/schema/
https://uor.foundation/op/
https://uor.foundation/cert/
https://uor.foundation/observable/

Classes

Name	IRI	Subclass Of	Comment
ComputationTrace	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2002/07/owl#Thing`	A complete record of a kernel computation: the input, output, every operation step, and accumulated metrics.
ComputationStep	`https://uor.foundation/trace/ComputationStep`	`http://www.w3.org/2002/07/owl#Thing`	A single step in a computation trace: one operation applied to produce one output from one or more inputs.
TraceMetrics	`https://uor.foundation/trace/TraceMetrics`	`http://www.w3.org/2002/07/owl#Thing`	Summary metrics for a computation trace: total steps, accumulated ring distance, and accumulated Hamming distance.
GeodesicTrace	`https://uor.foundation/trace/GeodesicTrace`	`https://uor.foundation/trace/ComputationTrace`	A computation trace that satisfies the dual geodesic condition (GD_1): AR_1-ordered and DC_10-selected. The path of least dissipation through the resolution landscape.
GeodesicViolation	`https://uor.foundation/trace/GeodesicViolation`	`http://www.w3.org/2002/07/owl#Thing`	A record of a geodesic condition violation at a specific step of a computation trace. Produced by GeodesicValidator when J_k(step_i) < max_\{free\} J_k(state_i).
MeasurementEvent	`https://uor.foundation/trace/MeasurementEvent`	`https://uor.foundation/trace/ComputationStep`	A specialized computation step recording a single projective collapse of a SuperposedSiteState. Carries pre-collapse entropy and post-collapse Landauer cost (QM_1).
MeasurementOutcome	`https://uor.foundation/trace/MeasurementOutcome`	`http://www.w3.org/2002/07/owl#Thing`	A single outcome of a projective measurement on a SuperposedSiteState, recording the classical site index (outcomeValue) and its Born-rule probability \|α_k\|² (outcomeProbability). Multiple outcomes form the probability distribution of a measurement.

Properties

Name	Kind	Functional	Domain	Range	Comment
input	Object	true	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/schema/Datum`	The input datum of this computation.
output	Object	true	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/schema/Datum`	The output datum of this computation.
step	Object	false	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/trace/ComputationStep`	A computation step in this trace.
monodromy	Object	true	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/observable/DihedralElement`	The monodromy accumulated by this computation: the net dihedral group element produced by the full operation sequence.
from	Object	true	`https://uor.foundation/trace/ComputationStep`	`https://uor.foundation/schema/Datum`	The input datum of this computation step.
to	Object	true	`https://uor.foundation/trace/ComputationStep`	`https://uor.foundation/schema/Datum`	The output datum of this computation step.
operation	Object	true	`https://uor.foundation/trace/ComputationStep`	`https://uor.foundation/op/Operation`	The operation applied in this computation step.
index	Datatype	true	`https://uor.foundation/trace/ComputationStep`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The zero-based sequential index of this step within its trace.
stepCount	Datatype	true	`https://uor.foundation/trace/TraceMetrics`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Total number of computation steps in this trace.
totalRingDistance	Datatype	true	`https://uor.foundation/trace/TraceMetrics`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Total ring-metric distance accumulated across all steps.
totalHammingDistance	Datatype	true	`https://uor.foundation/trace/TraceMetrics`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	Total Hamming-metric distance accumulated across all steps.
certifiedBy	Object	true	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/cert/Certificate`	The certificate that attests to the correctness of this computation trace.
residualEntropy	Object	true	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/observable/ResidualEntropy`	The residual entropy observable remaining after this computation trace, linking to the ThermoObservable taxonomy (TH_9 connection).
isGeodesic	Datatype	true	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this computation trace satisfies the dual geodesic condition (GD_1): AR_1-ordered and DC_10-selected.
geodesicCertificate	Object	true	`https://uor.foundation/trace/GeodesicTrace`	`https://uor.foundation/cert/GeodesicCertificate`	The GeodesicCertificate attesting that this trace satisfied both GD_1 conditions.
geodesicViolation	Object	false	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/trace/GeodesicViolation`	A GeodesicViolation record indicating where the trace deviated from the geodesic condition.
stepEntropyCost	Datatype	true	`https://uor.foundation/trace/ComputationStep`	`http://www.w3.org/2001/XMLSchema#decimal`	The entropy cost of a single computation step. On a geodesic, this equals ln 2 for every step (GD_2).
cumulativeEntropyCost	Datatype	true	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2001/XMLSchema#decimal`	The total entropy cost accumulated across all steps of a trace. On a geodesic, equals freeRank_initial × ln 2 (GD_3).
jacobianAtStep	Datatype	true	`https://uor.foundation/trace/ComputationStep`	`http://www.w3.org/2001/XMLSchema#decimal`	The Jacobian value J_k at this step, used by the GeodesicValidator to check DC_10 maximality.
adiabaticallyOrdered	Datatype	true	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether the step sequence of this trace follows the AR_1 adiabatic ordering (decreasing freeRank × cost-per-site).
violationReason	Datatype	true	`https://uor.foundation/trace/GeodesicViolation`	`http://www.w3.org/2001/XMLSchema#string`	Human-readable description of why a geodesic violation occurred, citing the step index and the unused higher-J_k option.
measurementEvent	Object	false	`https://uor.foundation/trace/ComputationTrace`	`https://uor.foundation/trace/MeasurementEvent`	A MeasurementEvent step within this computation trace.
preCollapseEntropy	Datatype	true	`https://uor.foundation/trace/MeasurementEvent`	`http://www.w3.org/2001/XMLSchema#decimal`	The von Neumann entropy S_vN of the SuperposedSiteState before projective collapse.
postCollapseLandauerCost	Datatype	true	`https://uor.foundation/trace/MeasurementEvent`	`http://www.w3.org/2001/XMLSchema#decimal`	The Landauer cost incurred by the projective collapse. Equals preCollapseEntropy at β* = ln 2 (QM_1).
collapseStep	Datatype	true	`https://uor.foundation/trace/MeasurementEvent`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The step index within the enclosing ComputationTrace at which this projective collapse occurred.
amplitudeVector	Datatype	true	`https://uor.foundation/trace/MeasurementEvent`	`http://www.w3.org/2001/XMLSchema#decimal`	The full pre-collapse amplitude vector of all branches at the time of measurement. Enables Born rule verification (QM_5): P(outcome k) = \|α_k\|² / Σ\|αᵢ\|².
isAR1Ordered	Datatype	true	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether this computation trace has steps ordered by the AR_1 adiabatic metric (decreasing freeRank × cost-per-site). One of the two sub-predicates of isGeodesic (GD_6).
isDC10Selected	Datatype	true	`https://uor.foundation/trace/ComputationTrace`	`http://www.w3.org/2001/XMLSchema#boolean`	Whether each step of this computation trace was selected by the DC_10 Jacobian criterion (maximal J_k among free sites). One of the two sub-predicates of isGeodesic (GD_6).
outcomeValue	Datatype	true	`https://uor.foundation/trace/MeasurementOutcome`	`http://www.w3.org/2001/XMLSchema#nonNegativeInteger`	The classical site index selected by projective collapse in this measurement outcome.
outcomeProbability	Datatype	true	`https://uor.foundation/trace/MeasurementOutcome`	`http://www.w3.org/2001/XMLSchema#decimal`	The Born-rule probability of this measurement outcome: \|α_k\|² where α_k is the amplitude of the collapsed site.

Named Individuals

Name	Type	Properties	Comment
geodesic_Q0	`https://uor.foundation/trace/GeodesicTrace`	`isGeodesic`: true `adiabaticallyOrdered`: true	Canonical geodesic trace at quantum level Q0 (n=8). Demonstrates GD_1 through GD_3 at the base level.
geodesic_Q1	`https://uor.foundation/trace/GeodesicTrace`	`isGeodesic`: true `adiabaticallyOrdered`: true	Canonical geodesic trace at quantum level Q1 (n=16). Demonstrates geodesic scaling from Q0 to Q1.
geodesic_Q2	`https://uor.foundation/trace/GeodesicTrace`	`isGeodesic`: true `adiabaticallyOrdered`: true	Canonical geodesic trace at quantum level Q2 (n=32). Demonstrates geodesic scaling from Q1 to Q2.
geodesic_Q3	`https://uor.foundation/trace/GeodesicTrace`	`isGeodesic`: true `adiabaticallyOrdered`: true	Canonical geodesic trace at quantum level Q3 (n=64). Demonstrates geodesic scaling from Q2 to Q3.
collapse_equal_superposition	`https://uor.foundation/trace/MeasurementEvent`	`preCollapseEntropy`: 0.693147 `postCollapseLandauerCost`: 0.693147	Canonical measurement event: collapse of an equal superposition (\|α\|² = 0.5). Maximum von Neumann entropy S_vN = ln 2. Maximum Landauer cost per QM_1.
collapse_biased	`https://uor.foundation/trace/MeasurementEvent`	`preCollapseEntropy`: 0.325083 `postCollapseLandauerCost`: 0.325083	Canonical measurement event: collapse of a biased superposition (\|α\|² = 0.9). Lower entropy than equal superposition. Demonstrates QM_3 bound.
collapse_classical	`https://uor.foundation/trace/MeasurementEvent`	`preCollapseEntropy`: 0.0 `postCollapseLandauerCost`: 0.0	Canonical measurement event: collapse of a classical state (\|α\|² = 1). Zero entropy, zero Landauer cost. Demonstrates QM_4 idempotence.