Triple

T5191842
Position Surface form Disambiguated ID Type / Status
Subject Charles Hermite E117173 entity
Predicate knownFor P22 FINISHED
Object 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.
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 functions | Statement: [Charles Hermite, knownFor, Hermite functions]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hermite functions
Context triple: [Charles Hermite, knownFor, Hermite functions]
  • A. 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.
  • B. 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.
  • C. Wightman functions
    Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
  • D. Daubechies wavelets
    Daubechies wavelets are a family of compactly supported orthogonal wavelets widely used in signal processing and image compression for their efficient time-frequency localization.
  • E. Chebyshev functions
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • 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 functions
Triple: [Charles Hermite, knownFor, Hermite functions]
Generated description
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.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Hermite functions
Target entity description: 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.
  • A. 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.
  • B. 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.
  • C. Wightman functions
    Wightman functions are vacuum expectation values of time-ordered products of quantum fields that rigorously encode the correlation structure and axiomatic foundations of relativistic quantum field theory.
  • D. Daubechies wavelets
    Daubechies wavelets are a family of compactly supported orthogonal wavelets widely used in signal processing and image compression for their efficient time-frequency localization.
  • E. Chebyshev functions
    Chebyshev functions are arithmetic functions in number theory that encode information about the distribution of prime numbers and play a key role in analytic approaches to the prime number theorem.
  • 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_69bd44620ff48190bcac01782107a397 completed March 20, 2026, 12:58 p.m.
NER Named-entity recognition batch_69bd79ed61c88190bda492f6489f44de completed March 20, 2026, 4:46 p.m.
NED1 Entity disambiguation (via context triple) batch_69bee0943ce48190838aff0cfd12c655 completed March 21, 2026, 6:16 p.m.
NEDg Description generation batch_69bee5fc0c408190b4ad4b77e0045182 completed March 21, 2026, 6:39 p.m.
NED2 Entity disambiguation (via description) batch_69bee6b954c08190a353ebcfe829888a completed March 21, 2026, 6:43 p.m.
Created at: March 20, 2026, 1:46 p.m.