Triple

T2364680
Position Surface form Disambiguated ID Type / Status
Subject Riemann–Liouville integral E47352 entity
Predicate comparedWith P278 FINISHED
Object Weyl fractional integral
The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
E259778 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: Weyl fractional integral | Statement: [Riemann–Liouville integral, comparedWith, Weyl fractional integral]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Weyl fractional integral
Context triple: [Riemann–Liouville integral, comparedWith, Weyl fractional integral]
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • 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. Weierstrass function
    The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
  • D. Wigner distribution function
    The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
  • E. Weyl quantization
    Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
  • 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: Weyl fractional integral
Triple: [Riemann–Liouville integral, comparedWith, Weyl fractional integral]
Generated description
The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Weyl fractional integral
Target entity description: The Weyl fractional integral is a generalization of the classical integral to arbitrary (including non-integer) orders, defined on periodic functions or the whole real line and used in fractional calculus to model memory and hereditary properties in various systems.
  • A. Riemann–Liouville integral
    The Riemann–Liouville integral is a fundamental operator in fractional calculus that generalizes the concept of an n-fold repeated integral to non-integer (fractional) orders.
  • 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. Weierstrass function
    The Weierstrass function is a classic example in mathematical analysis of a continuous function that is nowhere differentiable, illustrating the counterintuitive behavior possible in real-valued functions.
  • D. Wigner distribution function
    The Wigner distribution function is a quasi-probability distribution used in quantum mechanics and signal processing to represent quantum states in phase space, often exhibiting non-classical features such as negative values.
  • E. Weyl quantization
    Weyl quantization is a mathematical procedure in quantum mechanics that systematically associates classical observables with quantum operators in a symmetric and coordinate-independent way.
  • 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_69a88a1a4a6081908645b0f2914521ab completed March 4, 2026, 7:38 p.m.
NER Named-entity recognition batch_69abc7486cb48190acef1891cc87bdb1 completed March 7, 2026, 6:35 a.m.
NED1 Entity disambiguation (via context triple) batch_69aea896e0388190aabff2d70787dc43 completed March 9, 2026, 11:01 a.m.
NEDg Description generation batch_69aea91ce164819091aa24b287f9fb8e completed March 9, 2026, 11:03 a.m.
NED2 Entity disambiguation (via description) batch_69aea999b864819084134c670e7c5d9c completed March 9, 2026, 11:06 a.m.
Created at: March 4, 2026, 7:55 p.m.