Triple

T15562307
Position Surface form Disambiguated ID Type / Status
Subject Lippmann–Schwinger equation E371027 entity
Predicate relatedTo P37 FINISHED
Object Møller operators
Møller operators are mathematical operators in quantum scattering theory that connect free particle states to interacting scattering states, enabling the formulation of asymptotic in and out states.
E1163514 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: Møller operators | Statement: [Lippmann–Schwinger equation, relatedTo, Møller operators]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Møller operators
Context triple: [Lippmann–Schwinger equation, relatedTo, Møller operators]
  • A. 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.
  • 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. Operational Methods in Mathematical Physics
    Operational Methods in Mathematical Physics is a classic mathematical physics text by Harold Jeffreys that develops and applies operational calculus techniques to solve differential equations and other problems in theoretical physics.
  • D. Friedrichs extension
    The Friedrichs extension is a fundamental construction in functional analysis that associates a unique self-adjoint extension to certain symmetric, semibounded operators, playing a key role in the mathematical formulation of quantum mechanics and partial differential equations.
  • E. Stone’s theorem on one-parameter unitary groups
    Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • 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: Møller operators
Triple: [Lippmann–Schwinger equation, relatedTo, Møller operators]
Generated description
Møller operators are mathematical operators in quantum scattering theory that connect free particle states to interacting scattering states, enabling the formulation of asymptotic in and out states.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Møller operators
Target entity description: Møller operators are mathematical operators in quantum scattering theory that connect free particle states to interacting scattering states, enabling the formulation of asymptotic in and out states.
  • A. 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.
  • 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. Operational Methods in Mathematical Physics
    Operational Methods in Mathematical Physics is a classic mathematical physics text by Harold Jeffreys that develops and applies operational calculus techniques to solve differential equations and other problems in theoretical physics.
  • D. Friedrichs extension
    The Friedrichs extension is a fundamental construction in functional analysis that associates a unique self-adjoint extension to certain symmetric, semibounded operators, playing a key role in the mathematical formulation of quantum mechanics and partial differential equations.
  • E. Stone’s theorem on one-parameter unitary groups
    Stone’s theorem on one-parameter unitary groups is a fundamental result in functional analysis and quantum mechanics that characterizes strongly continuous one-parameter unitary groups as being generated by unique self-adjoint operators.
  • 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_69d85cc6cf40819091f4a5facee1ebe6 completed April 10, 2026, 2:13 a.m.
NER Named-entity recognition batch_69e04ddc66448190948280fb0c8d390c completed April 16, 2026, 2:47 a.m.
NED1 Entity disambiguation (via context triple) batch_69ff456821988190971539b683f6c656 completed May 9, 2026, 2:32 p.m.
NEDg Description generation batch_69ff46f44b2c81909f65f0ab455c6549 completed May 9, 2026, 2:38 p.m.
NED2 Entity disambiguation (via description) batch_69ff477a63b48190a453cf669dfda228 completed May 9, 2026, 2:40 p.m.
Created at: April 10, 2026, 4:09 a.m.