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.