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.