Triple

T10269882
Position Surface form Disambiguated ID Type / Status
Subject Wilhelm Blaschke E240805 entity
Predicate knownFor P22 FINISHED
Object Blaschke selection theorem
The Blaschke selection theorem is a fundamental result in convex geometry and functional analysis that guarantees the existence of a convergent subsequence in any bounded sequence of convex bodies under the Hausdorff metric.
E853120 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: Blaschke selection theorem | Statement: [Wilhelm Blaschke, knownFor, Blaschke selection theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Blaschke selection theorem
Context triple: [Wilhelm Blaschke, knownFor, Blaschke selection theorem]
  • A. Helly’s theorem
    Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
  • B. Krein–Milman theorem
    The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
  • C. Carathéodory’s theorem in convex geometry
    Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
  • D. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • E. Banach–Mazur theorem
    The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
  • 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: Blaschke selection theorem
Triple: [Wilhelm Blaschke, knownFor, Blaschke selection theorem]
Generated description
The Blaschke selection theorem is a fundamental result in convex geometry and functional analysis that guarantees the existence of a convergent subsequence in any bounded sequence of convex bodies under the Hausdorff metric.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Blaschke selection theorem
Target entity description: The Blaschke selection theorem is a fundamental result in convex geometry and functional analysis that guarantees the existence of a convergent subsequence in any bounded sequence of convex bodies under the Hausdorff metric.
  • A. Helly’s theorem
    Helly’s theorem is a fundamental result in convex geometry that gives conditions under which a family of convex sets in Euclidean space has a nonempty common intersection.
  • B. Krein–Milman theorem
    The Krein–Milman theorem is a fundamental result in functional analysis and convex geometry stating that a compact convex set in a locally convex topological vector space is the closed convex hull of its extreme points.
  • C. Carathéodory’s theorem in convex geometry
    Carathéodory’s theorem in convex geometry is a fundamental result stating that any point in the convex hull of a set in ℝⁿ can be expressed as a convex combination of at most n+1 points from that set.
  • D. Minkowski’s theorem on convex sets
    Minkowski’s theorem on convex sets is a fundamental result in convex geometry that characterizes lattice points in convex bodies, underpinning much of the theory of convex polytopes and the geometry of numbers.
  • E. Banach–Mazur theorem
    The Banach–Mazur theorem is a fundamental result in functional analysis that characterizes separable Banach spaces as isometrically isomorphic to closed subspaces of spaces of continuous functions on compact metric spaces.
  • 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_69d381a94c1881908fc38fc263d9b9c2 completed April 6, 2026, 9:49 a.m.
NER Named-entity recognition batch_69d4d270fb088190ba43b6f24e881b94 completed April 7, 2026, 9:46 a.m.
NED1 Entity disambiguation (via context triple) batch_69d6f80c25888190a3e8a2c513df7043 completed April 9, 2026, 12:51 a.m.
NEDg Description generation batch_69d6fcaca55c81908a48ac2a0ce24b85 completed April 9, 2026, 1:11 a.m.
NED2 Entity disambiguation (via description) batch_69d6fd772bc08190bf270f5fc767fb29 completed April 9, 2026, 1:14 a.m.
Created at: April 6, 2026, 11:35 a.m.