Triple
T5229396
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Klein–Gordon equation |
E118070
|
entity |
| Predicate | hasOperator |
P179
|
FINISHED |
| Object |
dAlembert operator
The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
|
E505995
|
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: dAlembert operator | Statement: [Klein–Gordon equation, hasOperator, dAlembert operator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: dAlembert operator Context triple: [Klein–Gordon equation, hasOperator, dAlembert operator]
-
A.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
-
B.
d’Alembert’s formula
d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
-
C.
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.
-
D.
d’Alembert’s principle
d’Alembert’s principle is a fundamental concept in classical mechanics that reformulates Newton’s laws to analyze the motion of systems by introducing inertial forces so they can be treated as if in static equilibrium.
-
E.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
- 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: dAlembert operator Triple: [Klein–Gordon equation, hasOperator, dAlembert operator]
Generated description
The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: dAlembert operator Target entity description: The d'Alembert operator is a second-order differential operator used in relativistic wave equations to describe how fields propagate through spacetime.
-
A.
Laplace operator
The Laplace operator is a second-order differential operator widely used in mathematics and physics to describe phenomena such as diffusion, heat flow, and wave propagation.
-
B.
d’Alembert’s formula
d’Alembert’s formula is a classical solution method for the one-dimensional wave equation that expresses the displacement of a vibrating string in terms of its initial shape and velocity.
-
C.
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.
-
D.
d’Alembert’s principle
d’Alembert’s principle is a fundamental concept in classical mechanics that reformulates Newton’s laws to analyze the motion of systems by introducing inertial forces so they can be treated as if in static equilibrium.
-
E.
Jacobi operator
The Jacobi operator is a linear differential operator central to the theory of elliptic functions and integrable systems, named after the mathematician Carl Gustav Jacob Jacobi.
- 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_69bd4466fb8c819083b806a79414d7e4 |
completed | March 20, 2026, 12:58 p.m. |
| NER | Named-entity recognition | batch_69bd7ae006ec8190abd23f650ca5bf53 |
completed | March 20, 2026, 4:50 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bef80ca924819095bcc729feb0e464 |
completed | March 21, 2026, 7:57 p.m. |
| NEDg | Description generation | batch_69bef8996a208190b9b84b297434c549 |
completed | March 21, 2026, 7:59 p.m. |
| NED2 | Entity disambiguation (via description) | batch_69bef935c2288190b2c66e25b8f065bd |
completed | March 21, 2026, 8:01 p.m. |
Created at: March 20, 2026, 1:48 p.m.