Triple
T5903318
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Airy disk |
E131279
|
entity |
| Predicate | describedBy |
P264
|
FINISHED |
| Object |
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.
|
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: Bessel functions | Statement: [Airy disk, describedBy, Bessel functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Bessel functions Context triple: [Airy disk, describedBy, Bessel functions]
-
A.
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.
-
B.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
-
C.
Jacobi elliptic functions
Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of 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.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
- 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: Bessel functions Triple: [Airy disk, describedBy, Bessel functions]
Generated description
Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Bessel functions Target entity description: Bessel functions are special mathematical functions that commonly arise as solutions to differential equations with cylindrical symmetry, widely used in physics and engineering.
-
A.
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.
-
B.
Fresnel integrals
Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
-
C.
Jacobi elliptic functions
Jacobi elliptic functions are a family of doubly periodic complex functions that generalize trigonometric functions and play a central role in the theory of elliptic integrals and many areas of 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.
Jacobi polynomials
Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
- 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_69c0085864a88190a569c05ff7d65f29 |
completed | March 22, 2026, 3:18 p.m. |
| NER | Named-entity recognition | batch_69c037376d5c8190a0a8457e07bebea8 |
completed | March 22, 2026, 6:38 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69c0b166b0bc8190a201899cf45a9b31 |
completed | March 23, 2026, 3:20 a.m. |
| NEDg | Description generation | batch_69c0b27438a08190ab6b72c8fd682bf6 |
completed | March 23, 2026, 3:24 a.m. |
| NED2 | Entity disambiguation (via description) | batch_69c0b309a70081908ad3e819879b17e4 |
completed | March 23, 2026, 3:27 a.m. |
Created at: March 22, 2026, 3:58 p.m.