Triple

T1615212
Position Surface form Disambiguated ID Type / Status
Subject Carl Gustav Jacob Jacobi E34700 entity
Predicate notableWork P4 FINISHED
Object 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.
E182748 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 elliptic functions | Statement: [Carl Gustav Jacob Jacobi, notableWork, Jacobi elliptic functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Jacobi elliptic functions
Context triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi elliptic functions]
  • A. 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.
  • B. 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.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • 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 elliptic functions
Triple: [Carl Gustav Jacob Jacobi, notableWork, Jacobi elliptic functions]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Jacobi elliptic functions
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. Gauss’s constant
    Gauss’s constant is a mathematical constant arising in number theory and complex analysis, particularly in connection with the lemniscate and elliptic functions.
  • D. Riemann–Siegel formula
    The Riemann–Siegel formula is an asymptotic expression that efficiently approximates the Riemann zeta function on the critical line, playing a key role in the numerical study of its zeros.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • 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_69a885ffc5ec819091afa325d5f9611c completed March 4, 2026, 7:20 p.m.
NER Named-entity recognition batch_69a9099049e0819099763ecb09fb4f57 completed March 5, 2026, 4:41 a.m.
NED1 Entity disambiguation (via context triple) batch_69ad51cd2e54819086924378792eb2e3 completed March 8, 2026, 10:39 a.m.
NEDg Description generation batch_69ad5248af2881909755ae87b4cd0041 completed March 8, 2026, 10:41 a.m.
NED2 Entity disambiguation (via description) batch_69ad52b3dcf081909e73fba891e985b2 completed March 8, 2026, 10:43 a.m.
Created at: March 4, 2026, 7:28 p.m.