Triple

T11398755
Position Surface form Disambiguated ID Type / Status
Subject brachistochrone problem E270049 entity
Predicate usesMethod P859 FINISHED
Object Euler–Lagrange differential equation E54267 NE FINISHED

How this triple was built (2 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 differential equation | Statement: [brachistochrone problem, usesMethod, Euler–Lagrange differential equation]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Euler–Lagrange differential equation
Context triple: [brachistochrone problem, usesMethod, Euler–Lagrange differential equation]
  • A. Euler–Lagrange equation chosen
    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.
  • B. Hamilton–Jacobi equation
    The Hamilton–Jacobi equation is a fundamental partial differential equation in classical mechanics that reformulates dynamics in terms of a generating function, providing a powerful bridge to quantum mechanics and modern analytical methods.
  • C. Lagrange multipliers
    Lagrange multipliers are a mathematical optimization technique used to find the extrema of functions subject to equality constraints.
  • D. Lagrangian function
    The Lagrangian function is a mathematical construct that combines an objective function with its constraints, widely used in optimization and variational calculus to analyze and solve constrained problems.
  • E. principle of least action
    The principle of least action is a fundamental concept in physics stating that the path taken by a physical system between two states is the one for which a specific quantity called the action is minimized (or made stationary), forming the basis of Lagrangian and Hamiltonian mechanics.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (3 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_69d6aacdbc6c8190af6dc3d5f5d22836 completed April 8, 2026, 7:21 p.m.
NER Named-entity recognition batch_69d8001adc188190ae45227856156412 completed April 9, 2026, 7:38 p.m.
NED1 Entity disambiguation (via context triple) batch_69e5b8250c288190b5bff70f7445b815 completed April 20, 2026, 5:22 a.m.
Created at: April 8, 2026, 9:34 p.m.