Triple

T6833480
Position Surface form Disambiguated ID Type / Status
Subject Bernoulli lemniscate E157392 entity
Predicate specialCaseOf P7025 FINISHED
Object Cassini oval
A Cassini oval is a plane algebraic curve consisting of all points whose product of distances to two fixed foci is constant, forming shapes that range from a single loop to a figure-eight.
E157392 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: Cassini oval | Statement: [Bernoulli lemniscate, specialCaseOf, Cassini oval]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Cassini oval
Context triple: [Bernoulli lemniscate, specialCaseOf, Cassini oval]
  • A. Bernoulli lemniscate
    The Bernoulli lemniscate is a figure-eight–shaped algebraic curve that serves as a classic example in the study of complex analysis, elliptic functions, and special constants.
  • B. Tusi couple
    The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
  • C. Ellipse
    The Ellipse is a large, oval-shaped public park and ceremonial lawn just south of the White House in Washington, D.C., often used for national events and recreation.
  • D. Cartesian circle
    The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
  • E. 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.
  • 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: Cassini oval
Triple: [Bernoulli lemniscate, specialCaseOf, Cassini oval]
Generated description
A Cassini oval is a plane algebraic curve consisting of all points whose product of distances to two fixed foci is constant, forming shapes that range from a single loop to a figure-eight.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Cassini oval
Target entity description: A Cassini oval is a plane algebraic curve consisting of all points whose product of distances to two fixed foci is constant, forming shapes that range from a single loop to a figure-eight.
  • A. Bernoulli lemniscate chosen
    The Bernoulli lemniscate is a figure-eight–shaped algebraic curve that serves as a classic example in the study of complex analysis, elliptic functions, and special constants.
  • B. Tusi couple
    The Tusi couple is a geometric device from medieval Islamic astronomy that generates linear motion from the sum of two circular motions, later influencing Copernican models of planetary motion.
  • C. Ellipse
    The Ellipse is a large, oval-shaped public park and ceremonial lawn just south of the White House in Washington, D.C., often used for national events and recreation.
  • D. Cartesian circle
    The Cartesian circle is a famous alleged circular reasoning in René Descartes’ Meditations, where his proof of God’s existence and his justification of clear and distinct perceptions appear to depend on each other.
  • E. 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.
  • F. None of above.

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_69c6882c53608190b99aebef079b23bd completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d62b1e8c8190a81d91191a54b073 completed March 27, 2026, 7:10 p.m.
NED1 Entity disambiguation (via context triple) batch_69c723fd50c88190af005fd58ca0aee6 completed March 28, 2026, 12:42 a.m.
NEDg Description generation batch_69c7247806808190ac60c134cec612c8 completed March 28, 2026, 12:44 a.m.
NED2 Entity disambiguation (via description) batch_69c7253b94f081909e7cee870a12af6b completed March 28, 2026, 12:47 a.m.
Created at: March 27, 2026, 2:18 p.m.