Triple
T18495159
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Hardy space |
E451925
|
entity |
| Predicate | hasOperator |
P179
|
FINISHED |
| Object | Toeplitz operator |
—
|
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: Toeplitz operator | Statement: [Hardy space, hasOperator, Toeplitz operator]
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Toeplitz operator Context triple: [Hardy space, hasOperator, Toeplitz operator]
-
A.
Toeplitz matrices
chosen
Toeplitz matrices are structured matrices whose entries are constant along each diagonal, playing a central role in operator theory, numerical analysis, and signal processing.
-
B.
Hilbert–Schmidt operators
Hilbert–Schmidt operators are a class of compact operators on Hilbert spaces characterized by having finite Hilbert–Schmidt norm, playing a central role in functional analysis and operator theory.
-
C.
Szegő kernel
The Szegő kernel is a fundamental reproducing kernel in complex analysis and operator theory, associated with Hardy spaces on the boundary of a domain and central to the study of orthogonal polynomials and boundary behavior of analytic functions.
-
D.
Fredholm operator
A Fredholm operator is a bounded linear operator between Banach (or Hilbert) spaces with finite-dimensional kernel and cokernel and a closed range, characterized by its integer-valued index.
-
E.
Steklov operator
The Steklov operator is a boundary integral operator arising in the study of elliptic partial differential equations and spectral problems, particularly in the context of Steklov eigenvalue problems.
- 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.