Triple

T18479298
Position Surface form Disambiguated ID Type / Status
Subject Cesàro summation E451514 entity
Predicate relatedTo P37 FINISHED
Object Hardy’s theory of divergent series — 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’s theory of divergent series | Statement: [Cesàro summation, relatedTo, Hardy’s theory of divergent series]
NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07 
Target entity: Hardy’s theory of divergent series
Context triple: [Cesàro summation, relatedTo, Hardy’s theory of divergent series]
  • A. Trigonometric Series, Vol. I
    Trigonometric Series, Vol. I is a foundational mathematical monograph by Antoni Zygmund that systematically develops the theory of trigonometric series and Fourier analysis.
  • B. Euler’s method of rearranging absolutely convergent series
    Euler’s method of rearranging absolutely convergent series is a technique introduced by Leonhard Euler to systematically reorder and manipulate convergent infinite series in order to derive new identities and product expansions, such as those appearing in analytic number theory.
  • C. theory of divergent series chosen
    The theory of divergent series is a branch of mathematical analysis that studies how to assign meaningful values to infinite series that do not converge in the usual sense, using specialized summation methods and analytic continuation.
  • D. Du Bois-Reymond theory of orders of infinity
    The Du Bois-Reymond theory of orders of infinity is a foundational framework in analysis that rigorously compares the growth rates of functions by classifying them into hierarchies of infinitesimal and infinite magnitudes.
  • E. Trigonometric Series, Vol. II
    "Trigonometric Series, Vol. II" is a classic advanced mathematics text by Antoni Zygmund that develops the modern theory of trigonometric series and Fourier analysis.
  • 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.