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.