Triple

T7978919
Position Surface form Disambiguated ID Type / Status
Subject Carl Gustav Jacob Jacobi E185515 entity
Predicate notableWork P4 FINISHED
Object 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.
E702055 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: Jacobi's inversion problem | Statement: [Carl Gustav Jacob Jacobi, notableWork, Jacobi's inversion problem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jacobi's inversion problem
Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi's inversion problem]
  • A. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • B. 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.
  • C. 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.
  • D. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • E. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • 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: Jacobi's inversion problem
Triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi's inversion problem]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jacobi's inversion problem
Target entity description: 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.
  • A. Jacobi elliptic functions
    Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of mathematical physics.
  • B. 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.
  • C. 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.
  • D. Hilbert’s twelfth problem
    Hilbert’s twelfth problem is one of David Hilbert’s famous list of 23 problems, asking for a general explicit class field theory that would generate all abelian extensions of a given number field using special values of analytic functions.
  • E. Introduction to the Theory of Algebraic Functions of One Variable
    Introduction to the Theory of Algebraic Functions of One Variable is a classic monograph by Claude Chevalley that provides a rigorous, modern foundation for the theory of algebraic function fields in one variable.
  • 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_69ca829851908190b4e03829353ee7c3 completed March 30, 2026, 2:03 p.m.
NER Named-entity recognition batch_69cb3bf84b1081908e60a556d984aad6 completed March 31, 2026, 3:14 a.m.
NED1 Entity disambiguation (via context triple) batch_69cbe0d3c724819087df03cea2ed998f completed March 31, 2026, 2:57 p.m.
NEDg Description generation batch_69cbe43e47048190a0044477f88de5d0 completed March 31, 2026, 3:11 p.m.
NED2 Entity disambiguation (via description) batch_69cc0d60254c819087d1de7ca6ea554b completed March 31, 2026, 6:07 p.m.
Created at: March 30, 2026, 5:14 p.m.