Triple

T18479412
Position Surface form Disambiguated ID Type / Status
Subject Tauberian theorems E451517 entity
Predicate hasSubtype P1244 FINISHED
Object Hardy–Littlewood 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: Hardy–Littlewood Tauberian theorems | Statement: [Tauberian theorems, hasSubtype, Hardy–Littlewood Tauberian theorems]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07
Target entity: Hardy–Littlewood Tauberian theorems
Context triple: [Tauberian theorems, hasSubtype, Hardy–Littlewood 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. Turán–Kubilius inequality
    The Turán–Kubilius inequality is a fundamental result in probabilistic number theory that provides bounds on the distribution of additive arithmetic functions.
  • C. Harmonic Analysis and the Theory of Probability
    Harmonic Analysis and the Theory of Probability is a seminal mathematical monograph that connects Fourier-analytic methods with probabilistic concepts, helping to lay the foundations of modern probability theory.
  • D. Cartwright–Littlewood theory on nonlinear differential equations
    Cartwright–Littlewood theory on nonlinear differential equations is a foundational body of work in dynamical systems that rigorously analyzed the complex, often chaotic behavior of solutions to nonlinear differential equations, particularly in the context of forced oscillations.
  • E. Carleson theorem on almost-everywhere convergence
    The Carleson theorem on almost-everywhere convergence is a fundamental result in harmonic analysis stating that the Fourier series of any square-integrable function on the circle converges almost everywhere to the function itself.
  • 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.