Triple
T22437975
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Bessel functions |
E554675
|
entity |
| Predicate | hasType |
P0
|
FINISHED |
| Object | Hankel functions |
—
|
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 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.
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 (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.