Triple

T7151277
Position Surface form Disambiguated ID Type / Status
Subject Hamiltonian (time translation generator) E166696 entity
Predicate isComponentOf P5722 FINISHED
Object four-momentum operator
The four-momentum operator is the relativistic quantum operator whose components generate spacetime translations, combining energy (via the Hamiltonian) and momentum into a single four-vector.
E646031 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: four-momentum operator | Statement: [Hamiltonian (time translation generator), isComponentOf, four-momentum operator]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: four-momentum operator
Context triple: [Hamiltonian (time translation generator), isComponentOf, four-momentum operator]
  • A. Dirac operator
    The Dirac operator is a fundamental first-order differential operator on spinor fields that generalizes the classical Dirac equation and plays a central role in geometry, topology, and quantum field theory.
  • B. dAlembert operator
    The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
  • C. Casimir operator
    The Casimir operator is a distinguished central element in the universal enveloping algebra of a Lie algebra that acts as a scalar on each irreducible representation and is used to classify and label those representations.
  • D. Dirac current
    Dirac current is the conserved four-current associated with the global U(1) symmetry of the Dirac field, representing the flow of probability (or charge) for relativistic spin-½ particles.
  • E. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • 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: four-momentum operator
Triple: [Hamiltonian (time translation generator), isComponentOf, four-momentum operator]
Generated description
The four-momentum operator is the relativistic quantum operator whose components generate spacetime translations, combining energy (via the Hamiltonian) and momentum into a single four-vector.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: four-momentum operator
Target entity description: The four-momentum operator is the relativistic quantum operator whose components generate spacetime translations, combining energy (via the Hamiltonian) and momentum into a single four-vector.
  • A. Dirac operator
    The Dirac operator is a fundamental first-order differential operator on spinor fields that generalizes the classical Dirac equation and plays a central role in geometry, topology, and quantum field theory.
  • B. dAlembert operator
    The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
  • C. Casimir operator
    The Casimir operator is a distinguished central element in the universal enveloping algebra of a Lie algebra that acts as a scalar on each irreducible representation and is used to classify and label those representations.
  • D. Dirac current
    Dirac current is the conserved four-current associated with the global U(1) symmetry of the Dirac field, representing the flow of probability (or charge) for relativistic spin-½ particles.
  • E. Poincaré group
    The Poincaré group is the fundamental symmetry group of special relativity, combining spacetime translations with Lorentz transformations in four-dimensional Minkowski space.
  • 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_69c68886779c8190a8e3fbabffe68253 completed March 27, 2026, 1:39 p.m.
NER Named-entity recognition batch_69c6e7f3e4a88190a3110f2368262528 completed March 27, 2026, 8:26 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7adad45208190a8e09173a4d26591 completed March 28, 2026, 10:30 a.m.
NEDg Description generation batch_69c7aeb1c59c8190b02fcb731003ad31 completed March 28, 2026, 10:34 a.m.
NED2 Entity disambiguation (via description) batch_69c7af2ad8a081909185cfd3a3d4e4d0 completed March 28, 2026, 10:36 a.m.
Created at: March 27, 2026, 2:46 p.m.