Triple

T6910707
Position Surface form Disambiguated ID Type / Status
Subject Hahn series E159923 entity
Predicate generalizes P2372 FINISHED
Object Laurent series
A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
E627725 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: Laurent series | Statement: [Hahn series, generalizes, Laurent series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Laurent series
Context triple: [Hahn series, generalizes, Laurent 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. 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.
  • C. Dirichlet series
    A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
  • D. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • 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: Laurent series
Triple: [Hahn series, generalizes, Laurent series]
Generated description
A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07
Target entity: Laurent series
Target entity description: A Laurent series is a representation of a complex function as a power series that can include terms with negative as well as nonnegative integer powers of the variable, typically used to describe behavior near singularities.
  • 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. 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.
  • C. Dirichlet series
    A Dirichlet series is an infinite series of the form ∑ aₙ/nˢ, fundamental in analytic number theory for studying arithmetic functions and L-functions.
  • D. Cauchy–Hadamard theorem
    The Cauchy–Hadamard theorem is a fundamental result in complex analysis that characterizes the radius of convergence of a power series in terms of the growth rate of its coefficients.
  • E. Mittag-Leffler function
    The Mittag-Leffler function is a complex function that generalizes the exponential function and plays a central role in fractional calculus and the theory of differential and integral equations.
  • 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_69c68839ccb88190b4aa5cc1aca3448f completed March 27, 2026, 1:38 p.m.
NER Named-entity recognition batch_69c6d9c135b48190b332aedf1d52bdb7 completed March 27, 2026, 7:25 p.m.
NED1 Entity disambiguation (via context triple) batch_69c7490c95548190a493d3fd23d1d7a5 completed March 28, 2026, 3:20 a.m.
NEDg Description generation batch_69c749d4b088819095f991f976592d04 completed March 28, 2026, 3:24 a.m.
NED2 Entity disambiguation (via description) batch_69c74aab12988190bd23cfcc06c55cde completed March 28, 2026, 3:27 a.m.
Created at: March 27, 2026, 2:25 p.m.