Triple

T7705125
Position Surface form Disambiguated ID Type / Status
Subject Kolmogorov distance E174592 entity
Predicate comparedWith P278 FINISHED
Object Lévy–Prokhorov metric
The Lévy–Prokhorov metric is a probability metric on the space of probability measures that metrizes weak convergence and is widely used in probability theory and measure theory.
E683051 NE FINISHED

How this triple was built (4 steps)

Every LLM step that produced this triple, in pipeline order — named-entity classification, the disambiguation choices (the exact options shown, with the pick highlighted), and the generated description. The batch + timestamp of each is in the Provenance table below.

NER Named-entity recognition gpt-5-mini
Instruction
Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).
Input
Phrase: Lévy–Prokhorov metric | Statement: [Kolmogorov distance, comparedWith, Lévy–Prokhorov metric]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lévy–Prokhorov metric
Context triple: [Kolmogorov distance, comparedWith, Lévy–Prokhorov metric]
  • A. Kolmogorov distance
    Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
  • B. Hausdorff metric
    The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
  • C. Banach–Mazur distance
    The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
  • D. Carathéodory measurability criterion
    The Carathéodory measurability criterion is a fundamental condition in measure theory that characterizes measurable sets via an outer measure by requiring additivity over intersections and complements.
  • E. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • F. None of above. chosen
  • G. Unsure - the case is ambiguous/there is not enough information to decide.
NEDg Description generation gpt-5.1
Instruction
Generate a one-sentence description of the target entity. 
You are given a context triple in the form (subject, predicate, object), where the object is the target entity. 
# Instructions
Use the triple to infer relevant information about the entity. Describe the entity based on what is most defining, well-known. 
Avoid repeating the information from the triple, unless really essential.
# Response Format
Return only the sentence: "Description: [one-sentence description of the target entity]"
Input
Entity: Lévy–Prokhorov metric
Triple: [Kolmogorov distance, comparedWith, Lévy–Prokhorov metric]
Generated description
The Lévy–Prokhorov metric is a probability metric on the space of probability measures that metrizes weak convergence and is widely used in probability theory and measure theory.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lévy–Prokhorov metric
Target entity description: The Lévy–Prokhorov metric is a probability metric on the space of probability measures that metrizes weak convergence and is widely used in probability theory and measure theory.
  • A. Kolmogorov distance
    Kolmogorov distance is a statistical metric that measures the maximum difference between two cumulative distribution functions, commonly used to quantify convergence in distribution and in goodness-of-fit tests.
  • B. Hausdorff metric
    The Hausdorff metric is a distance function that measures how far two subsets of a metric space are from each other, widely used in topology, geometry, and shape analysis.
  • C. Banach–Mazur distance
    The Banach–Mazur distance is a numerical measure in functional analysis that quantifies how "far apart" two finite-dimensional normed vector spaces are up to linear isomorphism.
  • D. Carathéodory measurability criterion
    The Carathéodory measurability criterion is a fundamental condition in measure theory that characterizes measurable sets via an outer measure by requiring additivity over intersections and complements.
  • E. Cameron–Martin theorem
    The Cameron–Martin theorem is a fundamental result in probability theory and functional analysis that characterizes how Gaussian measures on infinite-dimensional spaces change under shifts by elements of a special Hilbert subspace (the Cameron–Martin space).
  • F. None of above. chosen

Provenance (5 batches)

The batch behind each pipeline step, in order, with when it ran. Timestamps are batch-level — stages were processed in waves, so the object chain (NER → NED1 → NEDg → NED2) reads in order, but predicate / elicitation batches can sit in a different wave.

Step Stage Batch ID Status When
creating Elicitation batch_69c6995b3e8c8190833108f883d5f53c completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7028f17f0819081686ac146750d3a completed March 27, 2026, 10:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8acc088148190ba5ba07e4ad2284c completed March 29, 2026, 4:38 a.m.
NEDg Description generation batch_69c8ae313d4c8190964be233c0651f3a completed March 29, 2026, 4:44 a.m.
NED2 Entity disambiguation (via description) batch_69c8aea55c0081909aa0f6c96c8d6a03 completed March 29, 2026, 4:46 a.m.
Created at: March 27, 2026, 4:03 p.m.