Triple
T18479297
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Cesàro summation |
E451514
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Dirichlet series summation methods |
—
|
NE NERFINISHED |
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: Dirichlet series summation methods | Statement: [Cesàro summation, relatedTo, Dirichlet series summation methods]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet series summation methods Context triple: [Cesàro summation, relatedTo, Dirichlet series summation methods]
-
A.
Dirichlet series
chosen
A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
-
B.
Abel summation
Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
-
C.
Borel summation
Borel summation is a mathematical technique that assigns finite values to certain divergent series by transforming and analytically continuing their associated power series.
-
D.
Tauberian theorems
Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
-
E.
Selberg–Delange method results
Selberg–Delange method results are asymptotic formulas in analytic number theory that precisely describe the average order and distribution of multiplicative arithmetic functions using complex-analytic techniques.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
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_69d8d38465a0819099b9b42d2a662ac1 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e53065e8388190bb216dae89f8cf75 |
completed | April 19, 2026, 7:43 p.m. |
Created at: April 10, 2026, 11:35 a.m.