Triple
T18479220
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | theory of divergent series |
E451513
|
entity |
| Predicate | usesConcept |
P531
|
FINISHED |
| Object | Borel transform |
—
|
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: Borel transform | Statement: [theory of divergent series, usesConcept, Borel transform]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Borel transform Context triple: [theory of divergent series, usesConcept, Borel transform]
-
A.
Borel summation
chosen
Borel summation is a mathematical technique that assigns finite values to certain divergent series by transforming and analytically continuing their associated power series.
-
B.
Bailey transform
The Bailey transform is a technique in the theory of basic hypergeometric series that relates pairs of sequences (Bailey pairs) and underlies many identities and transformations in q-series and partition theory.
-
C.
Mellin transforms
Mellin transforms are integral transforms that convert functions into complex-variable representations, playing a central role in analytic number theory by linking arithmetic functions to Dirichlet series and zeta functions.
-
D.
Stieltjes transform
The Stieltjes transform is an integral transform that encodes a measure or distribution via a complex-analytic function, widely used in random matrix theory to study limiting spectral distributions and resolvents.
-
E.
Sommerfeld-Watson transform
The Sommerfeld-Watson transform is a complex-analysis technique that converts discrete sums over angular momentum into contour integrals, widely used in scattering theory and Regge theory to study analytic properties of amplitudes.
- 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.