Triple

T1358584
Position Surface form Disambiguated ID Type / Status
Subject Joseph-Louis Lagrange E29045 entity
Predicate knownFor P22 FINISHED
Object Lagrange interpolation polynomial
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
E156183 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: Lagrange interpolation polynomial | Statement: [Joseph-Louis Lagrange, knownFor, Lagrange interpolation polynomial]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Lagrange interpolation polynomial
Context triple: [Joseph-Louis Lagrange, knownFor, Lagrange interpolation polynomial]
  • A. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • B. Polynomial Root Finder
    Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
  • C. Weierstrass approximation theorem
    The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
  • 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. method of least squares
    The method of least squares is a fundamental mathematical technique for estimating unknown parameters by minimizing the sum of squared differences between observed and predicted values, widely used in statistics, data fitting, and regression analysis.
  • 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: Lagrange interpolation polynomial
Triple: [Joseph-Louis Lagrange, knownFor, Lagrange interpolation polynomial]
Generated description
The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Lagrange interpolation polynomial
Target entity description: The Lagrange interpolation polynomial is a classical formula in numerical analysis that constructs a unique polynomial passing through a given set of data points, widely used for interpolation and approximation.
  • A. Carathéodory–Fejér interpolation
    Carathéodory–Fejér interpolation is a classical result in complex analysis and approximation theory that concerns constructing analytic functions, typically with bounded or positive real part, that match prescribed initial Taylor coefficients.
  • B. Polynomial Root Finder
    Polynomial Root Finder is a TI-84 Plus calculator application that computes the roots of polynomial equations quickly and accurately.
  • C. Weierstrass approximation theorem
    The Weierstrass approximation theorem is a fundamental result in real analysis stating that any continuous function on a closed interval can be uniformly approximated by polynomials.
  • 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. method of least squares
    The method of least squares is a fundamental mathematical technique for estimating unknown parameters by minimizing the sum of squared differences between observed and predicted values, widely used in statistics, data fitting, and regression analysis.
  • 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_69a498d77abc8190913bf57e5f51d2c4 completed March 1, 2026, 7:51 p.m.
NER Named-entity recognition batch_69a4c28f5b988190b0be4504eabb919d completed March 1, 2026, 10:49 p.m.
NED1 Entity disambiguation (via context triple) batch_69acce701a84819094815ab6e8383b76 completed March 8, 2026, 1:18 a.m.
NEDg Description generation batch_69accf15d910819098e9a4b24247881b completed March 8, 2026, 1:21 a.m.
NED2 Entity disambiguation (via description) batch_69accff8af488190a7580cf7c02ceed9 completed March 8, 2026, 1:25 a.m.
Created at: March 1, 2026, 7:56 p.m.