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.