Triple

T22437975
Position Surface form Disambiguated ID Type / Status
Subject Bessel functions E554675 entity
Predicate hasType P0 FINISHED
Object Hankel functions
Hankel functions are specific complex-valued combinations of Bessel functions that represent outgoing and incoming cylindrical waves, widely used in solving wave propagation and scattering problems.
E554675 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 functions | Statement: [Bessel functions, hasType, Hankel functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hankel functions
Context triple: [Bessel functions, hasType, Hankel functions]
  • A. Bessel functions
    Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
  • B. 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.
  • C. Lommel polynomials
    Lommel polynomials are a family of special polynomials arising in the study of Bessel functions and certain differential equations in mathematical physics.
  • D. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • E. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • 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 functions
Triple: [Bessel functions, hasType, Hankel functions]
Generated description
Hankel functions are specific complex-valued combinations of Bessel functions that represent outgoing and incoming cylindrical waves, widely used in solving wave propagation and scattering problems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hankel functions
Target entity description: Hankel functions are specific complex-valued combinations of Bessel functions that represent outgoing and incoming cylindrical waves, widely used in solving wave propagation and scattering problems.
  • A. Bessel functions chosen
    Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
  • B. 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.
  • C. Lommel polynomials
    Lommel polynomials are a family of special polynomials arising in the study of Bessel functions and certain differential equations in mathematical physics.
  • D. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • E. Hardy Z-function
    The Hardy Z-function is a real-valued function derived from the Riemann zeta function on the critical line, used extensively in the study of the distribution of its zeros and the Riemann Hypothesis.
  • F. None of above.

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.