Triple
T4597251
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Kronecker’s lemma |
E100233
|
entity |
| Predicate | topic |
P261
|
FINISHED |
| Object | Cesàro-type averages |
E451514
|
NE FINISHED |
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: Cesàro-type averages | Statement: [Kronecker’s lemma, topic, Cesàro-type averages]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cesàro-type averages Context triple: [Kronecker’s lemma, topic, Cesàro-type averages]
-
A.
Cesàro summation
chosen
Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
-
B.
Tauberian theorems
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.
-
C.
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.
-
D.
Banach limit
A Banach limit is a linear functional on the space of bounded sequences that extends the usual limit and assigns generalized “limits” to sequences that may not converge in the classical sense.
-
E.
Khinchin–Kahane type inequalities
Khinchin–Kahane type inequalities are fundamental results in probability and functional analysis that bound moments or norms of random series (often with Rademacher or Gaussian coefficients) in terms of each other, providing powerful tools for studying the geometry of Banach spaces and random processes.
- F. None of above.
- G. Unsure - the case is ambiguous/there is not enough information to decide.
Provenance (3 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_69bd43cbc014819098b45f435908f88a |
completed | March 20, 2026, 12:55 p.m. |
| NER | Named-entity recognition | batch_69bd59420c108190b5c2c5039e964da5 |
completed | March 20, 2026, 2:27 p.m. |
| NED1 | Entity disambiguation (via context triple) | batch_69bdfa4a99c88190b7332fd2e1799b3a |
completed | March 21, 2026, 1:54 a.m. |
Created at: March 20, 2026, 1:11 p.m.