Triple
T20627469
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Schur algorithm |
E506855
|
entity |
| Predicate | relatedTo |
P37
|
FINISHED |
| Object | Herglotz functions |
—
|
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: Herglotz functions | Statement: [Schur algorithm, relatedTo, Herglotz functions]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Herglotz functions Context triple: [Schur algorithm, relatedTo, Herglotz functions]
-
A.
Herglotz functions
chosen
Herglotz functions are analytic functions on the upper half-plane with nonnegative imaginary part, central in complex analysis and operator theory due to their integral representation and role in moment and interpolation problems.
-
B.
Herglotz's theorem
Herglotz's theorem is a fundamental result in harmonic analysis and probability theory that characterizes positive-definite functions on the unit circle via representing measures.
-
C.
Blaschke products
Blaschke products are bounded analytic functions on the unit disk formed as (finite or infinite) products of Möbius transformations that map the disk to itself, playing a central role in complex analysis and function theory.
-
D.
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.
-
E.
Du Bois-Reymond function
The Du Bois-Reymond function is a classic example of a continuous but nowhere differentiable function, illustrating pathological behavior in real 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_69e0b4bd4a0081908d4e97a590a33fb2 |
completed | April 16, 2026, 10:06 a.m. |
| NER | Named-entity recognition | batch_69e6abe645888190b639ebedc5b3041a |
completed | April 20, 2026, 10:42 p.m. |
Created at: April 16, 2026, 11:42 a.m.