Triple

T11411746
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Levitan theory E270386 entity
Predicate relatedTo P37 FINISHED
Object Borg–Marchenko theorem
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
E924204 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: Borg–Marchenko theorem | Statement: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Borg–Marchenko theorem
Context triple: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
  • A. 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.
  • B. Bohr–Courant theorem
    The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
  • C. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • D. May–Wigner stability theorem
    The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
  • E. Szegő limit theorem
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • 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: Borg–Marchenko theorem
Triple: [Gelfand–Levitan theory, relatedTo, Borg–Marchenko theorem]
Generated description
The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Borg–Marchenko theorem
Target entity description: The Borg–Marchenko theorem is a fundamental result in inverse spectral theory that characterizes when a potential in a one-dimensional Schrödinger operator is uniquely determined by its spectral data.
  • A. 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.
  • B. Bohr–Courant theorem
    The Bohr–Courant theorem is a classical result in analytic number theory describing the value distribution of Dirichlet series, particularly the Riemann zeta function, and serves as a precursor to modern universality theorems such as Voronin’s.
  • C. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • D. May–Wigner stability theorem
    The May–Wigner stability theorem is a result in theoretical ecology and random matrix theory showing that large, complex systems with many random interactions are generically unstable beyond a critical level of complexity.
  • E. Szegő limit theorem
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • 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_69d6aaddeaa8819088b30ef7b50598c9 completed April 8, 2026, 7:22 p.m.
NER Named-entity recognition batch_69d8015017d08190b4020c76545556d6 completed April 9, 2026, 7:43 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b855f0508190a2e57ef9407ddb1a completed April 20, 2026, 5:23 a.m.
NEDg Description generation batch_69e5c28d3824819097ff84cb4e13c923 completed April 20, 2026, 6:07 a.m.
NED2 Entity disambiguation (via description) batch_69e5c451c6c88190bcbb1f54ede35d29 completed April 20, 2026, 6:14 a.m.
Created at: April 8, 2026, 9:34 p.m.