Triple

T2475514
Position Surface form Disambiguated ID Type / Status
Subject Israel Gelfand E55078 entity
Predicate knownFor P22 FINISHED
Object 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.
E270386 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: Gelfand–Levitan theory | Statement: [Israel Gelfand, knownFor, Gelfand–Levitan theory]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Gelfand–Levitan theory
Context triple: [Israel Gelfand, knownFor, Gelfand–Levitan theory]
  • 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. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • C. Wiener–Khinchin theorem
    The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
  • D. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • 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: Gelfand–Levitan theory
Triple: [Israel Gelfand, knownFor, Gelfand–Levitan theory]
Generated description
Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral equations.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Gelfand–Levitan theory
Target entity description: Gelfand–Levitan theory is a foundational framework in inverse spectral theory that reconstructs differential operators or potentials from their spectral data using integral 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. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • C. Wiener–Khinchin theorem
    The Wiener–Khinchin theorem is a fundamental result in signal processing and probability theory that relates a wide-sense stationary random process’s autocorrelation function to its power spectral density via the Fourier transform.
  • D. Selberg integral
    The Selberg integral is a fundamental multidimensional generalization of Euler’s beta integral that plays a central role in random matrix theory, combinatorics, and special functions.
  • 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_69ab49e279e88190ab10d7248aea9d11 completed March 6, 2026, 9:40 p.m.
NER Named-entity recognition batch_69abd14c8c388190bbdc486ffed6899e completed March 7, 2026, 7:18 a.m.
NED1 Entity disambiguation (via context triple) batch_69af17ab837881909bf8704acf9598e4 completed March 9, 2026, 6:55 p.m.
NEDg Description generation batch_69af1a8c7784819088be431513d60325 completed March 9, 2026, 7:07 p.m.
NED2 Entity disambiguation (via description) batch_69af1b10738881909b296ecd3ff53c1b completed March 9, 2026, 7:10 p.m.
Created at: March 6, 2026, 9:45 p.m.