Triple

T1190367
Position Surface form Disambiguated ID Type / Status
Subject Rudolf Peierls E25343 entity
Predicate notableIdea P4 FINISHED
Object 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.
E136243 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: Peierls bracket | Statement: [Rudolf Peierls, notableIdea, Peierls bracket]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Peierls bracket
Context triple: [Rudolf Peierls, notableIdea, Peierls bracket]
  • A. 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.
  • B. Tomonaga–Schwinger equation
    The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
  • C. Osterwalder–Schrader axioms
    The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
  • D. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • E. 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.
  • 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: Peierls bracket
Triple: [Rudolf Peierls, notableIdea, Peierls bracket]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Peierls bracket
Target entity description: 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.
  • A. 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.
  • B. Tomonaga–Schwinger equation
    The Tomonaga–Schwinger equation is a relativistic generalization of the Schrödinger equation that formulates quantum field evolution on arbitrary spacelike hypersurfaces, forming a key part of covariant quantum field theory.
  • C. Osterwalder–Schrader axioms
    The Osterwalder–Schrader axioms are a set of mathematical conditions that characterize Euclidean quantum field theories in a way that allows them to be rigorously continued to physically meaningful relativistic quantum field theories.
  • D. Wick’s theorem
    Wick’s theorem is a fundamental result in quantum field theory that expresses time-ordered products of field operators as sums of normal-ordered products with all possible contractions, forming the basis for deriving Feynman rules and diagrammatic expansions.
  • E. 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.
  • 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_69a49427d98881908646d6c63b8cea1e completed March 1, 2026, 7:31 p.m.
NER Named-entity recognition batch_69a4bd58d8d88190b8d9c9c9de7f4e97 completed March 1, 2026, 10:27 p.m.
NED1 Entity disambiguation (via context triple) batch_69ac764ccb1c8190a302137a0e67cb88 completed March 7, 2026, 7:02 p.m.
NEDg Description generation batch_69ac76e1b430819092669c6e83d7a62c completed March 7, 2026, 7:05 p.m.
NED2 Entity disambiguation (via description) batch_69ac77670fa08190827ef34ba9d52a70 completed March 7, 2026, 7:07 p.m.
Created at: March 1, 2026, 7:45 p.m.