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.