Triple
T6910707
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hahn series |
E159923
|
entity |
| Predicate | generalizes |
P2372
|
FINISHED |
| Object |
Laurent series
A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
|
E627725
|
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: Laurent series | Statement: [Hahn series, generalizes, Laurent series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Laurent series Context triple: [Hahn series, generalizes, Laurent series]
-
A.
Taylor series
A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
-
B.
Lambert series
Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
-
C.
Dirichlet series
A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
-
D.
Cauchy–Hadamard theorem
The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
-
E.
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.
- 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: Laurent series Triple: [Hahn series, generalizes, Laurent series]
Generated description
A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Laurent series Target entity description: A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
-
A.
Taylor series
A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
-
B.
Lambert series
Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
-
C.
Dirichlet series
A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
-
D.
Cauchy–Hadamard theorem
The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
-
E.
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.
- 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_69c68839ccb88190b4aa5cc1aca3448f |
completed | March 27, 2026, 1:38 p.m. |
| NER | Named-entity recognition | batch_69c6d9c135b48190b332aedf1d52bdb7 |
completed | March 27, 2026, 7:25 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c7490c95548190a493d3fd23d1d7a5 |
completed | March 28, 2026, 3:20 a.m. |
| NEDg | Description generation | batch_69c749d4b088819095f991f976592d04 |
completed | March 28, 2026, 3:24 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c74aab12988190bd23cfcc06c55cde |
completed | March 28, 2026, 3:27 a.m. |
Created at: March 27, 2026, 2:25 p.m.