Triple

T426762
Position Surface form Disambiguated ID Type / Status
Subject Leonhard Euler E9625 entity
Predicate notableWork P4 FINISHED
Object Euler–Lagrange equation
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
E54267 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: Euler–Lagrange equation | Statement: [Leonhard Euler, notableWork, Euler–Lagrange equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Euler–Lagrange equation
Context triple: [Leonhard Euler, notableWork, Euler–Lagrange equation]
  • A. Euler equations
    The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
  • B. Noether's theorem
    Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • E. Hessian forces
    Hessian forces were German auxiliary troops hired by the British Crown during the American Revolutionary War, known for their disciplined fighting and prominent role in key battles such as Trenton.
  • 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: Euler–Lagrange equation
Triple: [Leonhard Euler, notableWork, Euler–Lagrange equation]
Generated description
The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Euler–Lagrange equation
Target entity description: The Euler–Lagrange equation is a fundamental differential equation in the calculus of variations that provides the condition for a function to make a functional stationary, forming the basis of Lagrangian mechanics and many physical theories.
  • A. Euler equations
    The Euler equations are fundamental partial differential equations in fluid dynamics that describe the motion of an ideal (inviscid) fluid without viscosity.
  • B. Noether's theorem
    Noether's theorem is a fundamental result in theoretical physics and mathematics that links continuous symmetries of a physical system to corresponding conservation laws, such as energy or momentum conservation.
  • C. Feynman–Hellmann theorem
    The Feynman–Hellmann theorem is a result in quantum mechanics that relates the derivative of an energy eigenvalue with respect to a parameter in the Hamiltonian to the expectation value of the corresponding derivative of the Hamiltonian.
  • D. Fokker–Planck equation
    The Fokker–Planck equation is a partial differential equation that describes the time evolution of the probability density function of a stochastic (random) process, such as Brownian motion.
  • E. Hessian forces
    Hessian forces were German auxiliary troops hired by the British Crown during the American Revolutionary War, known for their disciplined fighting and prominent role in key battles such as Trenton.
  • 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_69a2e801e1d48190b505d1dd336b52ac completed Feb. 28, 2026, 1:05 p.m.
NER Named-entity recognition batch_69a2eed691c4819092b7e57306114bbc completed Feb. 28, 2026, 1:34 p.m.
NED1 Entity disambiguation (via context triple) batch_69a42f665c2881908850bce36cdf74b8 completed March 1, 2026, 12:21 p.m.
NEDg Description generation batch_69a43038d2348190a348e6661d27dde4 completed March 1, 2026, 12:25 p.m.
NED2 Entity disambiguation (via description) batch_69a430f6c6f88190b5aecfe3c4c8957d completed March 1, 2026, 12:28 p.m.
Created at: Feb. 28, 2026, 1:11 p.m.