Triple

T6800912
Position Surface form Disambiguated ID Type / Status
Subject Lagrange interpolation polynomial E156183 entity
Predicate relatedTo P37 FINISHED
Object Runge phenomenon
The Runge phenomenon is a numerical analysis effect where high-degree polynomial interpolation, especially at equally spaced points, produces large oscillations and poor approximations near the interval endpoints.
E620658 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: Runge phenomenon | Statement: [Lagrange interpolation polynomial, relatedTo, Runge phenomenon]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Runge phenomenon
Context triple: [Lagrange interpolation polynomial, relatedTo, Runge phenomenon]
  • A. 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.
  • B. 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.
  • C. Runge approximation theorem
    The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
  • D. Bernstein polynomials
    Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
  • E. Hermite interpolation
    Hermite interpolation is a numerical analysis method for constructing a polynomial that matches both function values and specified derivatives at given data points.
  • 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: Runge phenomenon
Triple: [Lagrange interpolation polynomial, relatedTo, Runge phenomenon]
Generated description
The Runge phenomenon is a numerical analysis effect where high-degree polynomial interpolation, especially at equally spaced points, produces large oscillations and poor approximations near the interval endpoints.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Runge phenomenon
Target entity description: The Runge phenomenon is a numerical analysis effect where high-degree polynomial interpolation, especially at equally spaced points, produces large oscillations and poor approximations near the interval endpoints.
  • A. 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.
  • B. 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.
  • C. Runge approximation theorem
    The Runge approximation theorem is a fundamental result in complex analysis stating that holomorphic functions on certain domains can be uniformly approximated by rational functions with poles outside those domains.
  • D. Bernstein polynomials
    Bernstein polynomials are a family of polynomials used in approximation theory that provide a constructive proof of the Weierstrass approximation theorem by uniformly approximating continuous functions on a closed interval.
  • E. Hermite interpolation
    Hermite interpolation is a numerical analysis method for constructing a polynomial that matches both function values and specified derivatives at given data points.
  • 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_69c68826e6a48190a3d220b541e639de completed March 27, 2026, 1:37 p.m.
NER Named-entity recognition batch_69c6d2e595188190a0bb4b595df3adb2 completed March 27, 2026, 6:56 p.m.
NED1 Entity disambiguation (via context triple) batch_69c71a9b0cc48190819380aeaf0228e7 completed March 28, 2026, 12:02 a.m.
NEDg Description generation batch_69c71d64c2fc8190abda8b5a0f57291b completed March 28, 2026, 12:14 a.m.
NED2 Entity disambiguation (via description) batch_69c71f3d4b8081908768c79642266431 completed March 28, 2026, 12:22 a.m.
Created at: March 27, 2026, 2:16 p.m.