Triple

T18479318
Position Surface form Disambiguated ID Type / Status
Subject Abel summation E451515 entity
Predicate relatedTo P37 FINISHED
Object Tauberian theorems — NE NERFINISHED

How this triple was built (2 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: Tauberian theorems | Statement: [Abel summation, relatedTo, Tauberian theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Tauberian theorems
Context triple: [Abel summation, relatedTo, Tauberian theorems]
  • A. Tauberian theorems chosen
    Tauberian theorems are results in mathematical analysis that connect the behavior of transformed series or integrals (such as those summed by Abel or Cesàro methods) back to the asymptotic behavior or convergence of the original sequences or series.
  • B. Szegő limit theorem
    The Szegő limit theorem is a fundamental result in analysis and operator theory that describes the asymptotic behavior of determinants of large Toeplitz matrices in terms of the symbol’s integral.
  • C. Abelian theorems
    Abelian theorems are results in mathematical analysis that deduce the behavior of a transformed function or series from known limiting behavior of the original one, typically in contrast to the inverse direction handled by Tauberian theorems.
  • D. Paley–Wiener theorem
    The Paley–Wiener theorem is a fundamental result in harmonic analysis that characterizes which functions arise as Fourier transforms of compactly supported functions (or distributions), linking analytic properties of entire functions with support properties in the original domain.
  • E. Abel’s theorem
    Abel’s theorem is a result in mathematical analysis that relates the behavior of power series at the boundary of their interval of convergence to the limit of their coefficients, providing conditions under which the sum of the series converges to a given value.
  • F. None of above.
  • G. Unsure - the case is ambiguous/there is not enough information to decide.

Provenance (2 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_69d8d38465a0819099b9b42d2a662ac1 completed April 10, 2026, 10:40 a.m.
NER Named-entity recognition batch_69e53065e8388190bb216dae89f8cf75 completed April 19, 2026, 7:43 p.m.
Created at: April 10, 2026, 11:35 a.m.