Triple

T10313545
Position Surface form Disambiguated ID Type / Status
Subject Herbert Busemann E241955 entity
Predicate hasConceptNamedAfter P3325 FINISHED
Object Busemann function
The Busemann function is a geometric tool in metric and Riemannian geometry that measures asymptotic distance along geodesic rays, often used to study the large-scale structure and boundaries of spaces.
E855796 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: Busemann function | Statement: [Herbert Busemann, hasConceptNamedAfter, Busemann function]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Busemann function
Context triple: [Herbert Busemann, hasConceptNamedAfter, Busemann function]
  • A. 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.
  • B. 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.
  • C. Bergman metric
    The Bergman metric is a canonical Kähler metric on complex domains derived from the Bergman kernel, widely used in several complex variables and complex differential geometry.
  • D. 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.
  • E. Kobayashi metric
    The Kobayashi metric is an intrinsic pseudometric in complex analysis that measures hyperbolic distance on complex manifolds and generalizes the Poincaré metric to higher dimensions.
  • 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: Busemann function
Triple: [Herbert Busemann, hasConceptNamedAfter, Busemann function]
Generated description
The Busemann function is a geometric tool in metric and Riemannian geometry that measures asymptotic distance along geodesic rays, often used to study the large-scale structure and boundaries of spaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Busemann function
Target entity description: The Busemann function is a geometric tool in metric and Riemannian geometry that measures asymptotic distance along geodesic rays, often used to study the large-scale structure and boundaries of spaces.
  • A. 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.
  • B. 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.
  • C. Bergman metric
    The Bergman metric is a canonical Kähler metric on complex domains derived from the Bergman kernel, widely used in several complex variables and complex differential geometry.
  • D. 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.
  • E. Kobayashi metric
    The Kobayashi metric is an intrinsic pseudometric in complex analysis that measures hyperbolic distance on complex manifolds and generalizes the Poincaré metric to higher dimensions.
  • 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_69d381ac38808190a8ca7457c85b625b completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d35a292c8190bc8c467e522bba92 completed April 7, 2026, 9:50 a.m.
NED1 Entity disambiguation (via context triple) batch_69d71d801978819097293b5c98350fef completed April 9, 2026, 3:31 a.m.
NEDg Description generation batch_69d73186831481909555e2205d8783a7 completed April 9, 2026, 4:56 a.m.
NED2 Entity disambiguation (via description) batch_69d732bfc76c819089287477b54a7b77 completed April 9, 2026, 5:01 a.m.
Created at: April 6, 2026, 11:48 a.m.