Triple
T18495147
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy space |
E451925
|
entity |
| Predicate | relatedConcept |
P37
|
FINISHED |
| Object | Blaschke product |
—
|
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: Blaschke product | Statement: [Hardy space, relatedConcept, Blaschke product]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Blaschke product Context triple: [Hardy space, relatedConcept, Blaschke product]
-
A.
Blaschke products
chosen
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.
-
B.
Koebe function
The Koebe function is a specific univalent holomorphic function on the unit disk that extremizes several classical bounds in geometric function theory, notably serving as the extremal example in the Koebe quarter theorem.
-
C.
Jensen’s formula
Jensen’s formula is a fundamental result in complex analysis that relates the values of an analytic function on a circle to the location and multiplicities of its zeros inside the disk.
-
D.
Borel–Carathéodory theorem
The Borel–Carathéodory theorem is a result in complex analysis that provides bounds on the modulus of a holomorphic function inside a disk in terms of the maximum of its real part on a larger concentric disk.
-
E.
Szegő polynomials
Szegő polynomials are a fundamental family of orthogonal polynomials on the unit circle that play a key role in complex analysis, approximation theory, and spectral theory.
- 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_69d8d3855d50819097fc8561b0299dd9 |
completed | April 10, 2026, 10:40 a.m. |
| NER | Named-entity recognition | batch_69e532bfeef4819096b2fa28abb662b9 |
completed | April 19, 2026, 7:53 p.m. |
Created at: April 10, 2026, 11:35 a.m.