Triple

T6482461
Position Surface form Disambiguated ID Type / Status
Subject Taylor series E146426 entity
Predicate specialCase P7025 FINISHED
Object Maclaurin series
The Maclaurin series is a power series expansion of a function about zero, expressing the function as an infinite sum of its derivatives at that point.
E146426 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: Maclaurin series | Statement: [Taylor series, specialCase, Maclaurin series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Maclaurin series
Context triple: [Taylor series, specialCase, Maclaurin series]
  • A. Taylor series
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • 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. Essai sur l’étude des fonctions données par leur développement de Taylor
    Essai sur l’étude des fonctions données par leur développement de Taylor is a foundational mathematical treatise by Jacques Hadamard that investigates the behavior and properties of functions defined through their Taylor series expansions.
  • D. Lambert series
    Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
  • E. Hadamard product (of power series)
    The Hadamard product (of power series) is an operation that forms a new power series by multiplying the corresponding coefficients of two given power series term by term.
  • 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: Maclaurin series
Triple: [Taylor series, specialCase, Maclaurin series]
Generated description
The Maclaurin series is a power series expansion of a function about zero, expressing the function as an infinite sum of its derivatives at that point.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Maclaurin series
Target entity description: The Maclaurin series is a power series expansion of a function about zero, expressing the function as an infinite sum of its derivatives at that point.
  • A. Taylor series chosen
    A Taylor series is an infinite sum of terms calculated from the derivatives of a function at a single point, used to represent and approximate functions as power series.
  • 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. Essai sur l’étude des fonctions données par leur développement de Taylor
    Essai sur l’étude des fonctions données par leur développement de Taylor is a foundational mathematical treatise by Jacques Hadamard that investigates the behavior and properties of functions defined through their Taylor series expansions.
  • D. Lambert series
    Lambert series are special infinite series in number theory and analysis, often involving arithmetic functions and powers of a variable, introduced by Johann Heinrich Lambert and used in the study of modular forms and q-series.
  • E. Hadamard product (of power series)
    The Hadamard product (of power series) is an operation that forms a new power series by multiplying the corresponding coefficients of two given power series term by term.
  • 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_69c0090158c08190af0df9a2348d2d52 completed March 22, 2026, 3:21 p.m.
NER Named-entity recognition batch_69c06a6cd0c4819085a921e6a361d91c completed March 22, 2026, 10:17 p.m.
NED1 Entity disambiguation (via context triple) batch_69c653afb1148190a8683f24a553f64d completed March 27, 2026, 9:53 a.m.
NEDg Description generation batch_69c6559d06c8819082cad37d62fcb3a3 completed March 27, 2026, 10:02 a.m.
NED2 Entity disambiguation (via description) batch_69c6564e01748190a3a12abcc0dfd30f completed March 27, 2026, 10:05 a.m.
Created at: March 22, 2026, 4:51 p.m.