Triple

T6858873

Position	Surface form	Disambiguated ID	Type / Status
Subject	Wiener filter	`E158221`	entity
Predicate	solves	`P14252`	FINISHED
Object	Wiener–Hopf equations Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.	`E624504`	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: Wiener–Hopf equations | Statement: [Wiener filter, solves, Wiener–Hopf equations]

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Wiener–Hopf equations
Context triple: [Wiener filter, solves, Wiener–Hopf equations]

A. The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
B. Introduction to the Study of Integral Equations
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
C. Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
D. Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
E. Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
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: Wiener–Hopf equations
Triple: [Wiener filter, solves, Wiener–Hopf equations]

Generated description

Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Wiener–Hopf equations
Target entity description: Wiener–Hopf equations are integral equations that arise in problems of filtering, prediction, and diffraction, forming the mathematical foundation for optimal linear filters such as the Wiener filter.

A. The Fourier Integral and Certain of Its Applications
The Fourier Integral and Certain of Its Applications is a foundational mathematical work by Norbert Wiener that develops and applies Fourier analysis to problems in harmonic analysis and related areas.
B. Introduction to the Study of Integral Equations
"Introduction to the Study of Integral Equations" is a foundational mathematical text by Maxime Bôcher that systematically develops the theory and applications of integral equations.
C. Gelfand–Levitan theory
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
D. Bhabha–Corben equations
The Bhabha–Corben equations are relativistic wave equations in quantum electrodynamics that describe the dynamics of spinning charged particles, developed by physicists Homi J. Bhabha and H. C. Corben.
E. Methods of Mathematical Physics
Methods of Mathematical Physics is a classic two-volume textbook by Richard Courant and David Hilbert that rigorously develops the mathematical foundations and techniques used in theoretical physics.
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_69c68830cdbc8190a8301c7a9d9f651a`	completed	March 27, 2026, 1:37 p.m.
NER	Named-entity recognition	`batch_69c6d8720bd48190adb446130a03d2bf`	completed	March 27, 2026, 7:20 p.m.
NED1	Entity disambiguation (via context triple)	`batch_69c72fe79af081909baacbfd4d5e8f24`	completed	March 28, 2026, 1:33 a.m.
NEDg	Description generation	`batch_69c7399b95e081908bbee3a598d6513c`	completed	March 28, 2026, 2:14 a.m.
NED2	Entity disambiguation (via description)	`batch_69c739f1b20c8190a8ef57357d4956b4`	completed	March 28, 2026, 2:16 a.m.

Created at: March 27, 2026, 2:21 p.m.