Triple
T10992351
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Dirichlet conditions |
E259780
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Dirichlet kernel |
E466248
|
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: Dirichlet kernel | Statement: [Dirichlet conditions, relatedTo, Dirichlet kernel]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet kernel Context triple: [Dirichlet conditions, relatedTo, Dirichlet kernel]
-
A.
Dirichlet kernel
chosen
The Dirichlet kernel is a trigonometric polynomial that arises in Fourier series as the summation kernel for partial sums, playing a key role in analyzing convergence properties.
-
B.
Poisson kernel
The Poisson kernel is a fundamental function in harmonic analysis and potential theory used to represent harmonic functions inside a domain from their boundary values, especially in the unit disk and upper half-plane.
-
C.
Dirichlet
Dirichlet was a 19th-century German mathematician renowned for foundational contributions to number theory and mathematical analysis, including Dirichlet's theorem on arithmetic progressions and the formalization of the concept of a function.
-
D.
Hermite functions
Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
-
E.
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.
- 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_69d6aa8a6a548190a750f944ccdc8064 |
completed | April 8, 2026, 7:20 p.m. |
| NER | Named-entity recognition | batch_69d795d32f9081909def643571499521 |
completed | April 9, 2026, 12:04 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69e34504ebec8190a78e4795765b0c24 |
completed | April 18, 2026, 8:47 a.m. |
Created at: April 8, 2026, 9:24 p.m.