Triple
T22437980
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bessel functions |
E554675
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Hankel transform |
—
|
NE NERFINISHED |
How this triple was built (3 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: Hankel transform | Statement: [Bessel functions, relatedTo, Hankel transform]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Hankel transform Context triple: [Bessel functions, relatedTo, Hankel transform]
-
A.
Bailey transform
The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
-
B.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
-
C.
Hilbert transform
The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
-
D.
Stieltjes transform
The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
-
E.
Walsh–Hadamard transform
The Walsh–Hadamard transform is an orthogonal, non-sinusoidal signal transform that decomposes data into a basis of square-wave-like functions, widely used in communications, coding theory, and signal processing.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Hankel transform Target entity description: The Hankel transform is an integral transform particularly suited to radially symmetric problems, using Bessel functions as its kernel to convert functions between spatial and frequency-like domains.
-
A.
Bailey transform
The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
-
B.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
-
C.
Hilbert transform
The Hilbert transform is an integral transform that produces the harmonic conjugate of a real-valued function, playing a central role in signal processing, harmonic analysis, and the theory of analytic signals.
-
D.
Stieltjes transform
The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
-
E.
Walsh–Hadamard transform
The Walsh–Hadamard transform is an orthogonal, non-sinusoidal signal transform that decomposes data into a basis of square-wave-like functions, widely used in communications, coding theory, and signal processing.
- F. None of above. chosen
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_69e11e5010e48190ae1e9c9db9697637 |
completed | April 16, 2026, 5:37 p.m. |
| NER | Named-entity recognition | batch_69f15adf52f08190a5b592be3e68af0f |
completed | April 29, 2026, 1:11 a.m. |
Created at: April 16, 2026, 8:47 p.m.