Triple
T4219682
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Stefan Banach |
E94307
|
entity |
| Predicate | eponymOf |
P12247
|
FINISHED |
| Object |
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.
|
E421065
|
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: Banach–Mazur distance | Statement: [Stefan Banach, eponymOf, Banach–Mazur distance]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Banach–Mazur distance Context triple: [Stefan Banach, eponymOf, Banach–Mazur distance]
-
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.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
C.
Carathéodory metric
The Carathéodory metric is an intrinsic distance function in complex analysis that measures how far apart points are in a domain based on holomorphic mappings into the unit disk.
-
D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
E.
Minkowski functional
The Minkowski functional is a mathematical tool in functional analysis that assigns a nonnegative real number to each vector in a vector space based on its position relative to a given convex, balanced, absorbing set, generalizing the notion of a norm.
- 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: Banach–Mazur distance Triple: [Stefan Banach, eponymOf, Banach–Mazur distance]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Banach–Mazur distance Target entity description: 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.
-
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.
Banach spaces
Banach spaces are complete normed vector spaces that provide a fundamental framework for functional analysis and the study of infinite-dimensional linear phenomena.
-
C.
Carathéodory metric
The Carathéodory metric is an intrinsic distance function in complex analysis that measures how far apart points are in a domain based on holomorphic mappings into the unit disk.
-
D.
Grothendieck inequality
The Grothendieck inequality is a fundamental result in functional analysis and theoretical computer science that bounds certain bilinear forms and has deep implications for Banach space theory, operator theory, and approximation algorithms.
-
E.
Minkowski functional
The Minkowski functional is a mathematical tool in functional analysis that assigns a nonnegative real number to each vector in a vector space based on its position relative to a given convex, balanced, absorbing set, generalizing the notion of a norm.
- 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_69b3451997e08190851db4a9a588837d |
completed | March 12, 2026, 10:58 p.m. |
| NER | Named-entity recognition | batch_69b34e0b2ee08190930600e1e802b325 |
completed | March 12, 2026, 11:36 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69b5963ffacc8190843b60ea1b224f91 |
completed | March 14, 2026, 5:09 p.m. |
| NEDg | Description generation | batch_69b596b7330081908c66a5a756531ffd |
completed | March 14, 2026, 5:11 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69b5976663d88190a73a729554e91074 |
completed | March 14, 2026, 5:14 p.m. |
Created at: March 12, 2026, 11:04 p.m.