Triple

T10313525
Position Surface form Disambiguated ID Type / Status
Subject Herbert Busemann E241955 entity
Predicate notableWork P4 FINISHED
Object Convex Surfaces
"Convex Surfaces" is a foundational mathematical monograph by Herbert Busemann that systematically develops the theory and geometry of convex surfaces.
E855793 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 Surfaces | Statement: [Herbert Busemann, notableWork, Convex Surfaces]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Convex Surfaces
Context triple: [Herbert Busemann, notableWork, Convex Surfaces]
  • A. Convex and Concave
    "Convex and Concave" is a 1955 lithograph print by M. C. Escher that depicts an architectural scene with impossible perspectives that can be interpreted in multiple, contradictory ways.
  • B. The Convexity of Hilltops
    "The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
  • C. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • D. Ellipsoids
    "Ellipsoids" is a sculptural series by German artist Isa Genzken that explores geometric abstraction through elongated, aerodynamic forms often associated with modern architecture and industrial design.
  • E. Smale’s paradox
    Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
  • 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 Surfaces
Triple: [Herbert Busemann, notableWork, Convex Surfaces]
Generated description
"Convex Surfaces" is a foundational mathematical monograph by Herbert Busemann that systematically develops the theory and geometry of convex surfaces.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Convex Surfaces
Target entity description: "Convex Surfaces" is a foundational mathematical monograph by Herbert Busemann that systematically develops the theory and geometry of convex surfaces.
  • A. Convex and Concave
    "Convex and Concave" is a 1955 lithograph print by M. C. Escher that depicts an architectural scene with impossible perspectives that can be interpreted in multiple, contradictory ways.
  • B. The Convexity of Hilltops
    "The Convexity of Hilltops" is a seminal geomorphological study by American geologist Grove Karl Gilbert that analyzes the shapes and formation processes of hilltops in relation to erosion and landscape evolution.
  • C. Clebsch diagonal surfaces
    Clebsch diagonal surfaces are classical 19th-century algebraic surfaces in projective three-space, famous as the first explicit smooth cubic surface with all 27 lines defined over the real numbers.
  • D. Ellipsoids
    "Ellipsoids" is a sculptural series by German artist Isa Genzken that explores geometric abstraction through elongated, aerodynamic forms often associated with modern architecture and industrial design.
  • E. Smale’s paradox
    Smale’s paradox is a result in differential topology showing that a sphere can be turned inside out in three-dimensional space through smooth deformations without tearing or creasing, challenging intuitive notions of geometry.
  • 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.