Triple

T23080556
Position Surface form Disambiguated ID Type / Status
Subject Eduard Study E575456 entity
Predicate notableConcept P201 FINISHED
Object Study quadric
The Study quadric is a fundamental algebraic variety in line geometry that represents the space of Euclidean rigid body motions via dual quaternions.
E1570244 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: Study quadric | Statement: [Eduard Study, notableConcept, Study quadric]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Study quadric
Context triple: [Eduard Study, notableConcept, Study quadric]
  • A. 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.
  • B. Rational Quadratic Forms
    Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
  • C. 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.
  • 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. 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.
  • 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: Study quadric
Triple: [Eduard Study, notableConcept, Study quadric]
Generated description
The Study quadric is a fundamental algebraic variety in line geometry that represents the space of Euclidean rigid body motions via dual quaternions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Study quadric
Target entity description: The Study quadric is a fundamental algebraic variety in line geometry that represents the space of Euclidean rigid body motions via dual quaternions.
  • A. 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.
  • B. Rational Quadratic Forms
    Rational Quadratic Forms is a classic monograph in number theory that systematically develops the arithmetic theory of quadratic forms over the rational numbers.
  • C. 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.
  • 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. 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.
  • 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_69e245be28d48190ad1348d5a73db37d completed April 17, 2026, 2:37 p.m.
NER Named-entity recognition batch_69f18c66a80481909ebc2ba69f1e4bd9 completed April 29, 2026, 4:43 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0c15b0a6ac819085f13e7bdc82840f completed May 19, 2026, 7:48 a.m.
NEDg Description generation batch_6a0c175e246081909d6451f245ccfe66 completed May 19, 2026, 7:55 a.m.
NED2 Entity disambiguation (via description) batch_6a0c1820a4d88190aed59f50b4e7ec47 completed May 19, 2026, 7:58 a.m.
Created at: April 17, 2026, 3:56 p.m.