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.