Triple
T27675237
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev polynomials of the first kind |
E697760
|
entity |
| Predicate | orthogonalWithRespectToWeight |
P76852
|
FINISHED |
| Object | w(x) = (1 - x^2)^(-1/2) |
—
|
LITERAL 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: w(x) = (1 - x^2)^(-1/2) | Statement: [Chebyshev polynomials of the first kind, orthogonalWithRespectToWeight, w(x) = (1 - x^2)^(-1/2)]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: orthogonalWithRespectToWeight Context triple: [Chebyshev polynomials of the first kind, orthogonalWithRespectToWeight, w(x) = (1 - x^2)^(-1/2)]
-
A.
orthogonalityProperty
chosen
Indicates that one entity possesses the property of being orthogonal (i.e., at right angles or having zero inner product) with respect to another entity or a given reference.
-
B.
orthonormalityRelation
Indicates that a set of vectors are mutually orthogonal and each has unit length with respect to a given inner product.
-
C.
areEigenfunctionsOf
Indicates that certain functions serve as eigenfunctions corresponding to a specified operator or transformation.
-
D.
representationWithRespectTo
Indicates a relationship in which one entity serves as a representation, depiction, or stand-in for another entity under a particular perspective, context, or interpretive framework.
-
E.
weightingFunction
Indicates a function that assigns relative importance or influence (weights) to elements within a set, often to adjust their impact in a calculation or decision process.
- F. None of above.
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_69ef590d458c81909583290c3cd0478b |
completed | April 27, 2026, 12:39 p.m. |
| NER | Named-entity recognition | batch_69f6359e3d3c81909814e2f0a7fb0ea9 |
completed | May 2, 2026, 5:34 p.m. |
| PD | Predicate disambiguation | batch_69f631871c888190bf29466fe4254e51 |
completed | May 2, 2026, 5:16 p.m. |
Created at: April 27, 2026, 2:43 p.m.