Triple

T22437980
Position Surface form Disambiguated ID Type / Status
Subject Bessel functions E554675 entity
Predicate relatedTo P37 FINISHED
Object Hankel transform
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.
E1536843 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: 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.
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: Hankel transform
Triple: [Bessel functions, relatedTo, Hankel transform]
Generated 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.
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 (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_69e11e5010e48190ae1e9c9db9697637 completed April 16, 2026, 5:37 p.m.
NER Named-entity recognition batch_69f15adf52f08190a5b592be3e68af0f completed April 29, 2026, 1:11 a.m.
NED1 Entity disambiguation (via context triple) batch_6a0b0c6d977c81909654774dc51ffb3a completed May 18, 2026, 12:56 p.m.
NEDg Description generation batch_6a0b0cfa58cc819085e976bf76fbf149 completed May 18, 2026, 12:58 p.m.
NED2 Entity disambiguation (via description) batch_6a0b0d534f1481908e74f754426d321f completed May 18, 2026, 1 p.m.
Created at: April 16, 2026, 8:47 p.m.