Triple

T16876413
Position Surface form Disambiguated ID Type / Status
Subject Finite Operator Calculus E421310 entity
Predicate relatedTo P37 FINISHED
Object Appell sequences
Appell sequences are special polynomial sequences characterized by a simple derivative property, where each polynomial’s derivative equals a constant multiple of the preceding one, making them fundamental in umbral and finite operator calculus.
E1237910 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: Appell sequences | Statement: [Finite Operator Calculus, relatedTo, Appell sequences]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Appell sequences
Context triple: [Finite Operator Calculus, relatedTo, Appell sequences]
  • A. 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.
  • B. Jack polynomials
    Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
  • C. 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.
  • D. 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.
  • E. Gegenbauer polynomials
    Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
  • 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: Appell sequences
Triple: [Finite Operator Calculus, relatedTo, Appell sequences]
Generated description
Appell sequences are special polynomial sequences characterized by a simple derivative property, where each polynomial’s derivative equals a constant multiple of the preceding one, making them fundamental in umbral and finite operator calculus.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Appell sequences
Target entity description: Appell sequences are special polynomial sequences characterized by a simple derivative property, where each polynomial’s derivative equals a constant multiple of the preceding one, making them fundamental in umbral and finite operator calculus.
  • A. 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.
  • B. Jack polynomials
    Jack polynomials are a family of symmetric polynomials depending on a continuous parameter that generalize several classical symmetric functions and play a key role in algebraic combinatorics, representation theory, and mathematical physics.
  • C. 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.
  • D. 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.
  • E. Gegenbauer polynomials
    Gegenbauer polynomials are a family of orthogonal polynomials on the interval [-1, 1] that generalize Legendre polynomials and play a key role in harmonic analysis and solutions of differential equations with spherical symmetry.
  • 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_69d889d470fc8190b4aec199636c0c56 completed April 10, 2026, 5:25 a.m.
NER Named-entity recognition batch_69e3b7f704a081909921d00b3c470472 completed April 18, 2026, 4:57 p.m.
NED1 Entity disambiguation (via context triple) batch_6a00c2b4abd08190841c5bb0b0eaa177 completed May 10, 2026, 5:39 p.m.
NEDg Description generation batch_6a00c355f4108190a4209599bf5f50da completed May 10, 2026, 5:41 p.m.
NED2 Entity disambiguation (via description) batch_6a00c413314881909e308588af09ce2a completed May 10, 2026, 5:44 p.m.
Created at: April 10, 2026, 5:29 a.m.