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.