Triple

T8399558
Position Surface form Disambiguated ID Type / Status
Subject Fresnel integrals E198136 entity
Predicate hasComponent P35 FINISHED
Object Fresnel cosine integral
The Fresnel cosine integral is a special function in mathematics that arises in wave optics and diffraction theory, defined by an integral involving the cosine of a quadratic argument.
E198136 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: Fresnel cosine integral | Statement: [Fresnel integrals, hasComponent, Fresnel cosine integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Fresnel cosine integral
Context triple: [Fresnel integrals, hasComponent, Fresnel cosine integral]
  • A. Fresnel integrals
    Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
  • B. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • C. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • D. 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.
  • E. 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.
  • 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: Fresnel cosine integral
Triple: [Fresnel integrals, hasComponent, Fresnel cosine integral]
Generated description
The Fresnel cosine integral is a special function in mathematics that arises in wave optics and diffraction theory, defined by an integral involving the cosine of a quadratic argument.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Fresnel cosine integral
Target entity description: The Fresnel cosine integral is a special function in mathematics that arises in wave optics and diffraction theory, defined by an integral involving the cosine of a quadratic argument.
  • A. Fresnel integrals chosen
    Fresnel integrals are special functions in mathematics that describe the complex oscillatory behavior of wave diffraction and interference, particularly in optics.
  • B. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • C. Riemann–Siegel theta function
    The Riemann–Siegel theta function is a special function that appears in the study of the Riemann zeta function, used to express its values on the critical line in a form suitable for high-precision numerical computation.
  • D. 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.
  • E. 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.
  • 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_69ca82f816bc8190ab321c07d72208c1 completed March 30, 2026, 2:04 p.m.
NER Named-entity recognition batch_69cb824bfcbc8190b26bfcb5f8c4777c completed March 31, 2026, 8:14 a.m.
NED1 Entity disambiguation (via context triple) batch_69ce02e129bc819081e6ea2dd43becba completed April 2, 2026, 5:47 a.m.
NEDg Description generation batch_69ce077f25648190b9a95fb72f5b4f8c completed April 2, 2026, 6:06 a.m.
NED2 Entity disambiguation (via description) batch_69ce08e192088190ad8170b1bedd568d completed April 2, 2026, 6:12 a.m.
Created at: March 30, 2026, 6:04 p.m.