Triple

T4461614
Position Surface form Disambiguated ID Type / Status
Subject Wigner distribution function E98266 entity
Predicate relatedTo P37 FINISHED
Object Moyal bracket
The Moyal bracket is a mathematical operation in phase-space quantum mechanics that generalizes the classical Poisson bracket to describe quantum corrections in the evolution of quasiprobability distributions.
E443157 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: Moyal bracket | Statement: [Wigner distribution function, relatedTo, Moyal bracket]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Moyal bracket
Context triple: [Wigner distribution function, relatedTo, Moyal bracket]
  • A. Peierls bracket
    The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
  • B. Jacobi bracket
    The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
  • C. Lie bracket
    The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
  • D. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • E. 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.
  • 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: Moyal bracket
Triple: [Wigner distribution function, relatedTo, Moyal bracket]
Generated description
The Moyal bracket is a mathematical operation in phase-space quantum mechanics that generalizes the classical Poisson bracket to describe quantum corrections in the evolution of quasiprobability distributions.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Moyal bracket
Target entity description: The Moyal bracket is a mathematical operation in phase-space quantum mechanics that generalizes the classical Poisson bracket to describe quantum corrections in the evolution of quasiprobability distributions.
  • A. Peierls bracket
    The Peierls bracket is a covariant generalization of the Poisson bracket used in quantum field theory and classical field theory to define commutation relations in a way that respects spacetime causality.
  • B. Jacobi bracket
    The Jacobi bracket is a bilinear operation generalizing the Poisson bracket in differential geometry, central to the theory of Jacobi manifolds and Hamiltonian systems.
  • C. Lie bracket
    The Lie bracket is a bilinear, antisymmetric operation on a Lie algebra that measures the noncommutativity of its elements and encodes its infinitesimal structure.
  • D. Weyl algebra
    The Weyl algebra is a fundamental noncommutative algebra generated by position and momentum operators satisfying canonical commutation relations, central in quantum mechanics and representation theory.
  • E. 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.
  • 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_69b3454a7c608190944f5455c8031d73 completed March 12, 2026, 10:59 p.m.
NER Named-entity recognition batch_69b35674f718819089388c3924dd1414 completed March 13, 2026, 12:12 a.m.
NED1 Entity disambiguation (via context triple) batch_69b6284b90708190b557b66bd7533f4e completed March 15, 2026, 3:32 a.m.
NEDg Description generation batch_69b629532cac8190b959adc0ef13305a completed March 15, 2026, 3:36 a.m.
NED2 Entity disambiguation (via description) batch_69b62d9c287c8190a305f9d21517f913 completed March 15, 2026, 3:55 a.m.
Created at: March 12, 2026, 11:34 p.m.