Triple
T20888615
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Sigma |
E514349
|
entity |
| Predicate | denotes |
P129
|
FINISHED |
| Object | Weierstrass sigma function (σ) |
—
|
NE NERFINISHED |
How this triple was built (3 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: Weierstrass sigma function (σ) | Statement: [Sigma, denotes, Weierstrass sigma function (σ)]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Weierstrass sigma function (σ) Context triple: [Sigma, denotes, Weierstrass sigma function (σ)]
-
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.
Dedekind eta function
The Dedekind eta function is a fundamental modular form in complex analysis and number theory, central to the theory of modular functions, partition identities, and connections with elliptic curves and string theory.
-
C.
Riemann–Siegel theta function
The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Jacobi theta functions
Jacobi theta functions are special functions in complex analysis and number theory that encode modular and elliptic properties, playing a central role in the theory of elliptic functions, modular forms, and various applications in mathematical physics.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Weierstrass sigma function (σ) Target entity description: The Weierstrass sigma function (σ) is an entire, quasi-periodic function associated with a given lattice in the complex plane, used in the theory of elliptic functions to construct and study related functions like the Weierstrass ℘-function.
-
A.
Weierstrass elliptic functions
chosen
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.
Dedekind eta function
The Dedekind eta function is a fundamental modular form in complex analysis and number theory, central to the theory of modular functions, partition identities, and connections with elliptic curves and string theory.
-
C.
Riemann–Siegel theta function
The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
-
D.
Mittag-Leffler function
The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
-
E.
Jacobi theta functions
Jacobi theta functions are special functions in complex analysis and number theory that encode modular and elliptic properties, playing a central role in the theory of elliptic functions, modular forms, and various applications in mathematical physics.
- F. None of above.
Provenance (2 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_69e0b4f7ebe48190952a85547a0f31a1 |
completed | April 16, 2026, 10:07 a.m. |
| NER | Named-entity recognition | batch_69e6d05be4a081908de0d3f5dbe4429a |
completed | April 21, 2026, 1:18 a.m. |
Created at: April 16, 2026, 12:46 p.m.