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.