Triple

T1380682
Position Surface form Disambiguated ID Type / Status
Subject Jean d’Alembert E29329 entity
Predicate knownFor P22 FINISHED
Object 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.
E158707 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: d’Alembert’s formula | Statement: [Jean d’Alembert, knownFor, d’Alembert’s formula]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: d’Alembert’s formula
Context triple: [Jean d’Alembert, knownFor, d’Alembert’s formula]
  • A. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • B. Laplace equation
    The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
  • C. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • D. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • 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: d’Alembert’s formula
Triple: [Jean d’Alembert, knownFor, d’Alembert’s formula]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: d’Alembert’s formula
Target entity description: 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.
  • A. Feynman–Kac formula
    The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
  • B. Laplace equation
    The Laplace equation is a fundamental second-order partial differential equation widely used in physics and engineering to describe steady-state phenomena such as electrostatics, gravitation, and heat conduction.
  • C. Riemann–Lebesgue lemma
    The Riemann–Lebesgue lemma is a fundamental result in Fourier analysis stating that the Fourier coefficients (or transform) of an integrable function vanish at infinity.
  • D. Euler–Maclaurin summation formula
    The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
  • E. Euler’s formula for complex exponentials
    Euler’s formula for complex exponentials is the fundamental identity \(e^{i\theta} = \cos\theta + i\sin\theta\), which links complex exponentials with trigonometric functions and underpins much of complex analysis and engineering mathematics.
  • 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_69a498d883a48190bfdca525296ef7ee completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c319f46481909ba8a69a19b865e5 completed March 1, 2026, 10:52 p.m.
NED1 Entity disambiguation (via context triple) batch_69acd48a48fc81908b156c273cb5dfc0 completed March 8, 2026, 1:44 a.m.
NEDg Description generation batch_69acd77d879881908decae7056bfd277 completed March 8, 2026, 1:57 a.m.
NED2 Entity disambiguation (via description) batch_69acd81c7c1081908b65ca5a57f8706e completed March 8, 2026, 1:59 a.m.
Created at: March 1, 2026, 7:59 p.m.