Triple
T9844226
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cauchy residue theorem |
E239298
|
entity |
| Predicate | isRelatedTo |
P37
|
FINISHED |
| Object | Laurent series |
E627725
|
NE FINISHED |
How this triple was built (2 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: [Cauchy residue theorem, isRelatedTo, Laurent series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Laurent series Context triple: [Cauchy residue theorem, isRelatedTo, Laurent series]
-
A.
Laurent series
chosen
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.
-
B.
Puiseux series
Puiseux series are formal power series in fractional powers of a variable, widely used in algebraic geometry and singularity theory to locally parametrize algebraic curves.
-
C.
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.
-
D.
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.
-
E.
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.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69ca84e3f0c48190ada72a65ebd50efd |
completed | March 30, 2026, 2:12 p.m. |
| NER | Named-entity recognition | batch_69cdb35dc29c819080203be5b904dc9d |
completed | April 2, 2026, 12:07 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69d1d5dda4b0819092703270e87bee5a |
completed | April 5, 2026, 3:24 a.m. |
Created at: March 30, 2026, 8:33 p.m.