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.