Triple

T11411739
Position Surface form Disambiguated ID Type / Status
Subject Gelfand–Levitan theory E270386 entity
Predicate appliesTo P1129 FINISHED
Object Schrödinger operators
Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
E924202 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: Schrödinger operators | Statement: [Gelfand–Levitan theory, appliesTo, Schrödinger operators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Schrödinger operators
Context triple: [Gelfand–Levitan theory, appliesTo, Schrödinger operators]
  • A. Schrödinger equation with point interactions
    The Schrödinger equation with point interactions is a quantum-mechanical model in which particles interact via idealized zero-range potentials, typically represented mathematically by Dirac delta functions.
  • B. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • C. Steklov operator
    The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
  • D. 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.
  • E. Sturm–Liouville problem
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • 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: Schrödinger operators
Triple: [Gelfand–Levitan theory, appliesTo, Schrödinger operators]
Generated description
Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Schrödinger operators
Target entity description: Schrödinger operators are a class of differential operators fundamental in quantum mechanics and spectral theory, used to describe the energy and dynamics of quantum systems.
  • A. Schrödinger equation with point interactions
    The Schrödinger equation with point interactions is a quantum-mechanical model in which particles interact via idealized zero-range potentials, typically represented mathematically by Dirac delta functions.
  • B. Hilbert–Schmidt operators
    Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
  • C. Steklov operator
    The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
  • D. 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.
  • E. Sturm–Liouville problem
    The Sturm–Liouville problem is a class of second-order linear differential equations with boundary conditions that yield real eigenvalues and orthogonal eigenfunctions forming a basis for function expansions in mathematical physics and engineering.
  • 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.