Triple
T4746244
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Peter Gustav Lejeune Dirichlet |
E105365
|
entity |
| Predicate | notableWork |
P4
|
FINISHED |
| Object |
Dirichlet test
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.
|
E466254
|
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: Dirichlet test | Statement: [Peter Gustav Lejeune Dirichlet, notableWork, Dirichlet test]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet test Context triple: [Peter Gustav Lejeune Dirichlet, notableWork, Dirichlet test]
-
A.
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.
-
B.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
C.
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.
-
D.
Dirichlet conditions
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
-
E.
Krak de l’Hospital
Krak de l’Hospital is an alternative name for Krak des Chevaliers, the famous medieval Crusader castle in Syria renowned for its massive fortifications and strategic importance.
- 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: Dirichlet test Triple: [Peter Gustav Lejeune Dirichlet, notableWork, Dirichlet test]
Generated description
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.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Dirichlet test Target entity description: 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.
-
A.
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.
-
B.
Riemann–Lebesgue lemma
The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
-
C.
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.
-
D.
Dirichlet conditions
Dirichlet conditions are a set of sufficient criteria on a function—such as piecewise continuity and having a finite number of extrema and discontinuities on an interval—that guarantee the convergence of its Fourier series representation.
-
E.
Krak de l’Hospital
Krak de l’Hospital is an alternative name for Krak des Chevaliers, the famous medieval Crusader castle in Syria renowned for its massive fortifications and strategic importance.
- 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_69bd43ef87a48190a5bc3600711aa032 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd64c3fcb081909b1fe867b4adac8b |
completed | March 20, 2026, 3:16 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69be3a40bee88190ae97f6d409b51e96 |
completed | March 21, 2026, 6:27 a.m. |
| NEDg | Description generation | batch_69be3af59ef88190a5acc493978d412e |
completed | March 21, 2026, 6:30 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69be3c8533fc8190b512d3fec34e7e28 |
completed | March 21, 2026, 6:36 a.m. |
Created at: March 20, 2026, 1:20 p.m.