Triple
T19051003
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet test |
E466254
|
entity |
| Predicate | hasVariant |
P455
|
FINISHED |
| Object | Dirichlet test for improper integrals |
—
|
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 test for improper integrals | Statement: [Dirichlet test, hasVariant, Dirichlet test for improper integrals]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet test for improper integrals Context triple: [Dirichlet test, hasVariant, Dirichlet test for improper integrals]
-
A.
Dirichlet test
chosen
The Dirichlet test is a criterion in mathematical analysis that provides sufficient conditions for the convergence of certain infinite series, particularly those involving oscillatory terms.
-
B.
Cauchy’s integral test
Cauchy’s integral test is a convergence criterion in mathematical analysis that determines whether an infinite series converges by relating it to the behavior of a corresponding improper integral.
-
C.
Cauchy condensation test
The Cauchy condensation test is a convergence criterion in mathematical analysis that determines whether an infinite series with positive, nonincreasing terms converges by comparing it to a related series formed by powers of two.
-
D.
Dini test for convergence of Fourier series
The Dini test for convergence of Fourier series is a classical criterion in harmonic analysis that gives sufficient conditions, involving the behavior of a function near a point, to ensure the pointwise convergence of its Fourier series there.
-
E.
Weierstrass M-test
The Weierstrass M-test is a criterion in real and complex analysis that provides a sufficient condition for the uniform convergence of a series of functions by comparing it to a convergent series of bounding constants.
- 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_69d8dd040fb881909af2a964f65ad208 |
completed | April 10, 2026, 11:20 a.m. |
| NER | Named-entity recognition | batch_69e5dc02597c8190b39fd2c7b7e42258 |
completed | April 20, 2026, 7:55 a.m. |
Created at: April 10, 2026, 12:03 p.m.