Triple
T12011612
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hassler Whitney |
E285916
|
entity |
| Predicate | notableFor |
P22
|
FINISHED |
| Object |
Whitney umbrella surface
The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
|
E960590
|
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: Whitney umbrella surface | Statement: [Hassler Whitney, notableFor, Whitney umbrella surface]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Whitney umbrella surface Context triple: [Hassler Whitney, notableFor, Whitney umbrella surface]
-
A.
Cayley surface
The Cayley surface is a classical cubic ruled surface in projective three-dimensional space, studied in algebraic geometry and named after the mathematician Arthur Cayley.
-
B.
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.
-
C.
Fermat surface
A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
-
D.
Kummer surfaces
Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
-
E.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
- 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: Whitney umbrella surface Triple: [Hassler Whitney, notableFor, Whitney umbrella surface]
Generated description
The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Whitney umbrella surface Target entity description: The Whitney umbrella surface is a classic example in singularity theory and differential topology, illustrating a self-intersecting surface with a pinch point singularity in three-dimensional space.
-
A.
Cayley surface
The Cayley surface is a classical cubic ruled surface in projective three-dimensional space, studied in algebraic geometry and named after the mathematician Arthur Cayley.
-
B.
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.
-
C.
Fermat surface
A Fermat surface is an algebraic surface in projective space defined by a homogeneous equation where each variable appears with the same exponent, generalizing the notion of Fermat curves to higher dimensions.
-
D.
Kummer surfaces
Kummer surfaces are special quartic algebraic surfaces in projective three-space characterized by having 16 ordinary double points, extensively studied in the context of complex geometry and abelian varieties.
-
E.
Klein quartic
The Klein quartic is a highly symmetric algebraic curve of genus 3 that plays a central role in complex geometry, group theory, and the study of Riemann surfaces.
- 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_69d6ab45a368819084fce08bf0dc3705 |
completed | April 8, 2026, 7:23 p.m. |
| NER | Named-entity recognition | batch_69d903d7777481908cd5a001f75e2ee3 |
completed | April 10, 2026, 2:06 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69f48b363c6481908c8414c1eecc14f5 |
completed | May 1, 2026, 11:15 a.m. |
| NEDg | Description generation | batch_69f48fc6da4c81908442f18cb4a65b27 |
completed | May 1, 2026, 11:34 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69f495cc50908190aab4f8ca64c66ef3 |
completed | May 1, 2026, noon |
Created at: April 8, 2026, 9:46 p.m.