Triple

T21610206
Position Surface form Disambiguated ID Type / Status
Subject Jakob Steiner E533284 entity
Predicate notableWork P4 FINISHED
Object Steiner surface
The Steiner surface is a classical quartic algebraic surface in projective three-space, notable for being a singular model of the real projective plane studied extensively in 19th-century geometry.
E1493310 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: Steiner surface | Statement: [Jakob Steiner, notableWork, Steiner surface]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Steiner surface
Context triple: [Jakob Steiner, notableWork, Steiner 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. 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.
  • 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. 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.
  • E. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • 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: Steiner surface
Triple: [Jakob Steiner, notableWork, Steiner surface]
Generated description
The Steiner surface is a classical quartic algebraic surface in projective three-space, notable for being a singular model of the real projective plane studied extensively in 19th-century geometry.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Steiner surface
Target entity description: The Steiner surface is a classical quartic algebraic surface in projective three-space, notable for being a singular model of the real projective plane studied extensively in 19th-century geometry.
  • 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. 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.
  • 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. 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.
  • E. Clebsch
    Clebsch is a German surname most notably associated with mathematician Alfred Clebsch, known for his contributions to algebraic geometry and invariant theory.
  • 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_69e0c46411108190bba0d4176dffc9f3 completed April 16, 2026, 11:13 a.m.
NER Named-entity recognition batch_69ef17e7d1388190922a90cb91ec9fc4 completed April 27, 2026, 8:01 a.m.
NED1 Entity disambiguation (via context triple) batch_6a09fd3d0d9881909d04a901cf65c211 completed May 17, 2026, 5:39 p.m.
NEDg Description generation batch_6a0a0c1bb6188190966c2db0f61048f7 completed May 17, 2026, 6:42 p.m.
NED2 Entity disambiguation (via description) batch_6a0a0cb1b9d08190aa0edccd5a49b289 completed May 17, 2026, 6:45 p.m.
Created at: April 16, 2026, 6:33 p.m.