Triple

T16876410
Position Surface form Disambiguated ID Type / Status
Subject Finite Operator Calculus E421310 entity
Predicate usesConcept P531 FINISHED
Object umbral calculus
Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
E1237908 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: umbral calculus | Statement: [Finite Operator Calculus, usesConcept, umbral calculus]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: umbral calculus
Context triple: [Finite Operator Calculus, usesConcept, umbral calculus]
  • A. Mueller calculus
    Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
  • B. 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.
  • C. 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.
  • D. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • E. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • 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: umbral calculus
Triple: [Finite Operator Calculus, usesConcept, umbral calculus]
Generated description
Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: umbral calculus
Target entity description: Umbral calculus is a mathematical framework that manipulates sequences of polynomials and linear operators using symbolic rules that resemble the manipulation of powers in classical algebra.
  • A. Mueller calculus
    Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
  • B. 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.
  • C. 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.
  • D. Bernoulli numbers
    Bernoulli numbers are a sequence of rational numbers that play a central role in number theory and analysis, especially in formulas for sums of powers of integers and in the study of special functions like the Riemann zeta function.
  • E. Gauss hypergeometric function
    The Gauss hypergeometric function is a special function defined by a power series that generalizes many elementary and higher transcendental functions and plays a central role in mathematical analysis, differential equations, and mathematical physics.
  • 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.