Triple
T18479417
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Tauberian theorems |
E451517
|
entity |
| Predicate | hasSubtype |
P1244
|
FINISHED |
| Object | Delange 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: Delange Tauberian theorems | Statement: [Tauberian theorems, hasSubtype, Delange Tauberian theorems]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Delange Tauberian theorems Context triple: [Tauberian theorems, hasSubtype, Delange 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.
Fejér’s theorem on Fourier series
Fejér’s theorem on Fourier series is a fundamental result in harmonic analysis stating that the Cesàro means (Fejér means) of the Fourier series of a continuous periodic function always converge uniformly to the function itself.
-
C.
Mertens’ theorems
Mertens’ theorems are classical results in analytic number theory that give precise asymptotic estimates for sums involving the Möbius function and the reciprocals of primes, illuminating the distribution of primes and their connection to the Riemann zeta function.
-
D.
Pisier’s factorization theorems
Pisier’s factorization theorems are fundamental results in functional analysis and operator theory that provide deep factorization properties for linear and multilinear operators on Banach spaces, extending and refining ideas related to Grothendieck-type inequalities.
-
E.
Dirichlet theorem on Fourier series
The Dirichlet theorem on Fourier series gives conditions under which a periodic function can be represented by a convergent Fourier series, specifying how and where the series converges to the function.
- 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.