Triple
T19285078
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Fourier series |
E482288
|
entity |
| Predicate | convergesUnderCondition |
P61769
|
FINISHED |
| Object | Dirichlet conditions |
—
|
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 conditions | Statement: [Fourier series, convergesUnderCondition, Dirichlet conditions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Dirichlet conditions Context triple: [Fourier series, convergesUnderCondition, Dirichlet conditions]
-
A.
Dirichlet conditions
chosen
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.
-
B.
Dirichlet theorem on Fourier series
The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
-
C.
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.
-
D.
Gibbs phenomenon
The Gibbs phenomenon is the persistent overshoot and oscillation that occurs near jump discontinuities when approximating a function with its Fourier series or other truncated series expansions.
-
E.
Dirichlet kernel
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.
- 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_69d8e8cf61b0819096fe3e4107827c4e |
completed | April 10, 2026, 12:10 p.m. |
| NER | Named-entity recognition | batch_69e5fc0152d48190b92272d4c7caa708 |
completed | April 20, 2026, 10:12 a.m. |
Created at: April 10, 2026, 1:30 p.m.