Triple

T7705205
Position Surface form Disambiguated ID Type / Status
Subject Edgeworth expansion E174595 entity
Predicate uses P98 FINISHED
Object Hermite polynomials
Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
E502189 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: Hermite polynomials | Statement: [Edgeworth expansion, uses, Hermite polynomials]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hermite polynomials
Context triple: [Edgeworth expansion, uses, Hermite polynomials]
  • A. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • B. Hermite functions
    Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
  • C. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • D. Orthogonal Polynomials
    Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
  • E. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • 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: Hermite polynomials
Triple: [Edgeworth expansion, uses, Hermite polynomials]
Generated description
Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hermite polynomials
Target entity description: Hermite polynomials are a classical family of orthogonal polynomials that arise prominently in probability theory, mathematical physics, and approximation methods such as the Edgeworth expansion.
  • A. Hermite
    Hermite is a French surname most famously associated with the 19th-century mathematician Charles Hermite, known for his contributions to number theory, algebra, and analysis.
  • B. Hermite functions chosen
    Hermite functions are a family of orthogonal functions built from Hermite polynomials and a Gaussian weight, widely used in quantum mechanics, signal processing, and approximation theory.
  • C. Jacobi polynomials
    Jacobi polynomials are a family of classical orthogonal polynomials depending on two parameters, widely used in approximation theory, numerical analysis, and solutions of differential equations.
  • D. Orthogonal Polynomials
    Orthogonal Polynomials is a classic mathematical monograph by Gábor Szegő that systematically develops the theory and applications of orthogonal polynomial systems in analysis and approximation theory.
  • E. Bernoulli polynomials
    Bernoulli polynomials are a sequence of polynomials deeply connected to number theory and analysis, appearing in the study of special functions, series expansions, and the evaluation of sums of powers of integers.
  • F. None of above.

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_69c6995b3e8c8190833108f883d5f53c completed March 27, 2026, 2:51 p.m.
NER Named-entity recognition batch_69c7028f17f0819081686ac146750d3a completed March 27, 2026, 10:19 p.m.
NED1 Entity disambiguation (via context triple) batch_69c8acc088148190ba5ba07e4ad2284c completed March 29, 2026, 4:38 a.m.
NEDg Description generation batch_69c8ae313d4c8190964be233c0651f3a completed March 29, 2026, 4:44 a.m.
NED2 Entity disambiguation (via description) batch_69c8aea55c0081909aa0f6c96c8d6a03 completed March 29, 2026, 4:46 a.m.
Created at: March 27, 2026, 4:03 p.m.