Triple
T4927204
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Weierstrass approximation theorem |
E110605
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Fourier series |
E173
|
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: Fourier series | Statement: [Weierstrass approximation theorem, relatedTo, Fourier series]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Fourier series Context triple: [Weierstrass approximation theorem, relatedTo, Fourier series]
-
A.
Fourier analysis
chosen
Fourier analysis is a mathematical method for decomposing functions or signals into sums of sinusoidal components, widely used in fields such as signal processing, physics, and engineering.
-
B.
Fourier
Fourier is a French surname most famously associated with Jean-Baptiste Joseph Fourier, the mathematician and physicist known for developing Fourier analysis and Fourier series.
-
C.
Fourier inversion theorem
The Fourier inversion theorem is a fundamental result in harmonic analysis that guarantees, under suitable conditions, that a function can be exactly reconstructed from its Fourier transform.
-
D.
FFT
FFT is the ICAO airline designator used in aviation to identify Frontier Airlines in flight plans and air traffic control communications.
-
E.
Poisson summation formula
The Poisson summation formula is a fundamental result in harmonic analysis that links sums of a function over the integers to sums of its Fourier transform, with deep applications in number theory, signal processing, and physics.
- 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_69bd4415190c8190817bee7ec9f9f944 |
completed | March 20, 2026, 12:56 p.m. |
| NER | Named-entity recognition | batch_69bd70354bd081909291a43439f42ed3 |
completed | March 20, 2026, 4:05 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69be77ac88148190a51fa2e9085d6897 |
completed | March 21, 2026, 10:49 a.m. |
Created at: March 20, 2026, 1:30 p.m.