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.