Triple
T17341089
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Banach limit |
E421066
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Cesàro summation |
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 summation | Statement: [Banach limit, relatedConcept, Cesàro summation]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Cesàro summation Context triple: [Banach limit, relatedConcept, Cesàro summation]
-
A.
Cesàro summation
chosen
Cesàro summation is a method of assigning finite values to certain divergent series by averaging their partial sums.
-
B.
Abel summation
Abel summation is a method in mathematical analysis for assigning values to certain divergent series by considering the limit of their power series as the variable approaches 1 from below.
-
C.
Borel summation
Borel summation is a mathematical technique that assigns finite values to certain divergent series by transforming and analytically continuing their associated power series.
-
D.
Euler–Maclaurin summation formula
The Euler–Maclaurin summation formula is a fundamental result in analysis that connects sums and integrals, providing powerful asymptotic expansions and error estimates for approximating series by integrals.
-
E.
Neumann series
The Neumann series is an infinite series expansion used to represent the inverse of an operator or solve integral and differential equations, analogous to a geometric series in functional analysis.
- 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_69d889d3adc881909319f1edb8d2a956 |
completed | April 10, 2026, 5:25 a.m. |
| NER | Named-entity recognition | batch_69e43a15f6488190ad7d489e7391ab12 |
completed | April 19, 2026, 2:12 a.m. |
| NED1 | Entity disambiguation (via context triple) | batch_6a018c588a7081909ab108cb4adfedfe |
completed | May 11, 2026, 7:59 a.m. |
Created at: April 10, 2026, 5:44 a.m.