Triple

T6833543
Position Surface form Disambiguated ID Type / Status
Subject arithmetic–geometric mean identities E157393 entity
Predicate relatedConcept P37 FINISHED
Object Landen transformations
Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
E621096 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: Landen transformations | Statement: [arithmetic–geometric mean identities, relatedConcept, Landen transformations]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Landen transformations
Context triple: [arithmetic–geometric mean identities, relatedConcept, Landen transformations]
  • A. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • B. Gale transform
    The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
  • C. Transformations
    "Transformations" is an influential art-critical work by British critic Roger Fry that explores the nature and evolution of modern art and aesthetic experience.
  • D. Transformations
    Transformations is a 1971 poetry collection by Anne Sexton that retells and darkly reimagines Grimm fairy tales through a confessional, feminist lens.
  • E. The Transformations Suite
    The Transformations Suite is a politically charged multimedia jazz composition by Samora Pinderhughes that explores themes of racial injustice, incarceration, and social transformation in contemporary America.
  • 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: Landen transformations
Triple: [arithmetic–geometric mean identities, relatedConcept, Landen transformations]
Generated description
Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Landen transformations
Target entity description: Landen transformations are classical iterative formulas in analysis that relate elliptic integrals (and associated means) at different moduli, enabling their efficient evaluation and simplification.
  • A. Sommerfeld-Watson transform
    The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
  • B. Gale transform
    The Gale transform is a construction in convex geometry and combinatorics that represents a finite point configuration or polytope in a dual space, often used to study their structural and combinatorial properties.
  • C. Transformations
    "Transformations" is an influential art-critical work by British critic Roger Fry that explores the nature and evolution of modern art and aesthetic experience.
  • D. Transformations
    Transformations is a 1971 poetry collection by Anne Sexton that retells and darkly reimagines Grimm fairy tales through a confessional, feminist lens.
  • E. The Transformations Suite
    The Transformations Suite is a politically charged multimedia jazz composition by Samora Pinderhughes that explores themes of racial injustice, incarceration, and social transformation in contemporary America.
  • 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_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.