Triple
T16991965
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Branko Grünbaum |
E412213
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Convex Polytopes
Convex Polytopes is a foundational mathematical monograph that systematically develops the theory, geometry, and combinatorics of convex polyhedra and higher-dimensional polytopes.
|
E1244435
|
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: Convex Polytopes | Statement: [Branko Grünbaum, notableWork, Convex Polytopes]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Convex Polytopes Context triple: [Branko Grünbaum, notableWork, Convex Polytopes]
-
A.
Polytopes
Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
-
B.
Regular Complex Polytopes
"Regular Complex Polytopes" is a seminal mathematical monograph by H. S. M. Coxeter that systematically develops the theory of regular polytopes in complex projective spaces.
-
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.
Regular Polytopes
"Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
-
E.
Borsuk’s conjecture in geometry
Borsuk’s conjecture in geometry is a famous (now disproven in higher dimensions) problem in metric geometry that proposed any bounded set in n-dimensional Euclidean space can be partitioned into n+1 subsets of smaller diameter.
- 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: Convex Polytopes Triple: [Branko Grünbaum, notableWork, Convex Polytopes]
Generated description
Convex Polytopes is a foundational mathematical monograph that systematically develops the theory, geometry, and combinatorics of convex polyhedra and higher-dimensional polytopes.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Convex Polytopes Target entity description: Convex Polytopes is a foundational mathematical monograph that systematically develops the theory, geometry, and combinatorics of convex polyhedra and higher-dimensional polytopes.
-
A.
Polytopes
Polytopes are large-scale multimedia architectural and musical installations created by Iannis Xenakis that combine sound, light, and spatial design into immersive, mathematically structured environments.
-
B.
Regular Complex Polytopes
"Regular Complex Polytopes" is a seminal mathematical monograph by H. S. M. Coxeter that systematically develops the theory of regular polytopes in complex projective spaces.
-
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.
Regular Polytopes
"Regular Polytopes" is a classic mathematical monograph by H. S. M. Coxeter that systematically develops the theory and classification of highly symmetric polytopes in various dimensions.
-
E.
Borsuk’s conjecture in geometry
Borsuk’s conjecture in geometry is a famous (now disproven in higher dimensions) problem in metric geometry that proposed any bounded set in n-dimensional Euclidean space can be partitioned into n+1 subsets of smaller diameter.
- 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_69d886cb581c8190ab05f4b429c9cd85 |
completed | April 10, 2026, 5:12 a.m. |
| NER | Named-entity recognition | batch_69e3d283d2388190a78bf8d179e83fdc |
completed | April 18, 2026, 6:50 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a00dc14d5688190945f7ae72f724922 |
completed | May 10, 2026, 7:27 p.m. |
| NEDg | Description generation | batch_6a0114d5aeb0819086f1a5d279ac0d0f |
completed | May 10, 2026, 11:29 p.m. |
| NED2 | Entity disambiguation (via description) | batch_6a0115c583608190bf07ac205399f253 |
completed | May 10, 2026, 11:33 p.m. |
Created at: April 10, 2026, 5:32 a.m.