Triple

T18729744
Position Surface form Disambiguated ID Type / Status
Subject Friedrich Richelot E458003 entity
Predicate notableWork P4 FINISHED
Object Richelot transformation of hyperelliptic integrals
The Richelot transformation of hyperelliptic integrals is a classical 19th-century method that relates and simplifies certain hyperelliptic integrals by transforming one hyperelliptic curve into another while preserving key integral properties.
E1340023 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: Richelot transformation of hyperelliptic integrals | Statement: [Friedrich Richelot, notableWork, Richelot transformation of hyperelliptic integrals]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Richelot transformation of hyperelliptic integrals
Context triple: [Friedrich Richelot, notableWork, Richelot transformation of hyperelliptic integrals]
  • A. Gauss transformation for elliptic integrals
    The Gauss transformation for elliptic integrals is a classical iterative procedure introduced by Carl Friedrich Gauss that relates and simplifies elliptic integrals via transformations closely connected to the arithmetic–geometric mean.
  • B. Baker’s theory of Abelian functions
    Baker’s theory of Abelian functions is a foundational mathematical work that systematically develops the theory of Abelian functions and their applications in complex analysis and algebraic geometry.
  • C. Jacobi's inversion problem
    Jacobi's inversion problem is a fundamental question in algebraic geometry and the theory of Abelian functions, concerning the inversion of Abelian integrals and the characterization of their multi-valued inverses.
  • D. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • E. Recherches sur les fonctions elliptiques
    Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
  • 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: Richelot transformation of hyperelliptic integrals
Triple: [Friedrich Richelot, notableWork, Richelot transformation of hyperelliptic integrals]
Generated description
The Richelot transformation of hyperelliptic integrals is a classical 19th-century method that relates and simplifies certain hyperelliptic integrals by transforming one hyperelliptic curve into another while preserving key integral properties.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Richelot transformation of hyperelliptic integrals
Target entity description: The Richelot transformation of hyperelliptic integrals is a classical 19th-century method that relates and simplifies certain hyperelliptic integrals by transforming one hyperelliptic curve into another while preserving key integral properties.
  • A. Gauss transformation for elliptic integrals
    The Gauss transformation for elliptic integrals is a classical iterative procedure introduced by Carl Friedrich Gauss that relates and simplifies elliptic integrals via transformations closely connected to the arithmetic–geometric mean.
  • B. Baker’s theory of Abelian functions
    Baker’s theory of Abelian functions is a foundational mathematical work that systematically develops the theory of Abelian functions and their applications in complex analysis and algebraic geometry.
  • C. Jacobi's inversion problem
    Jacobi's inversion problem is a fundamental question in algebraic geometry and the theory of Abelian functions, concerning the inversion of Abelian integrals and the characterization of their multi-valued inverses.
  • D. Weierstrass elliptic functions
    Weierstrass elliptic functions are a class of doubly periodic meromorphic functions that play a central role in the theory of elliptic curves and complex analysis.
  • E. Recherches sur les fonctions elliptiques
    Recherches sur les fonctions elliptiques is a foundational mathematical treatise by Niels Henrik Abel that significantly advanced the theory of elliptic functions and laid groundwork for modern complex analysis.
  • 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_69d8d393ba9c8190a8b03b04ddbb0a09 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e56d7660488190b4f70db963d05ef6 completed April 20, 2026, 12:04 a.m.
NED1 Entity disambiguation (via context triple) batch_6a05325b685c8190a2889755ed931973 completed May 14, 2026, 2:24 a.m.
NEDg Description generation batch_6a053410a8188190992d9fa6130ab372 completed May 14, 2026, 2:31 a.m.
NED2 Entity disambiguation (via description) batch_6a05349009e481909fb757415468aa70 completed May 14, 2026, 2:33 a.m.
Created at: April 10, 2026, 11:50 a.m.