Triple
T27675263
| Position | Surface form | Disambiguated ID | Type / Status |
|---|---|---|---|
| Subject | Chebyshev polynomials of the first kind |
E697760
|
entity |
| Predicate | orthogonalityNormalization |
P57348
|
FINISHED |
| Object | \int_{-1}^1 T_n(x)^2 (1-x^2)^{-1/2} dx = \pi for n=0 |
—
|
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: \int_{-1}^1 T_n(x)^2 (1-x^2)^{-1/2} dx = \pi for n=0 | Statement: [Chebyshev polynomials of the first kind, orthogonalityNormalization, \int_{-1}^1 T_n(x)^2 (1-x^2)^{-1/2} dx = \pi for n=0]
PD
Predicate disambiguation
gpt-5-mini-2025-08-07
Target predicate: orthogonalityNormalization
Context triple: [Chebyshev polynomials of the first kind, orthogonalityNormalization, \int_{-1}^1 T_n(x)^2 (1-x^2)^{-1/2} dx = \pi for n=0]
-
A.
orthogonalityProperty
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
chosen
Indicates that a set of vectors are mutually orthogonal and each has unit length with respect to a given inner product.
-
C.
normalizationInvolves
Indicates that a normalization process includes or makes use of a particular component, step, or element as part of its execution.
-
D.
nonOrthogonality
Indicates that two vectors, directions, or subspaces are not orthogonal, meaning their inner product is nonzero and they are not mutually perpendicular.
-
E.
refinesNormalization
Indicates that one normalization process or scheme improves, clarifies, or makes more precise another existing normalization.
- 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_69f63fd6c68481908c542aa03e297b9c |
completed | May 2, 2026, 6:17 p.m. |
| PD | Predicate disambiguation | batch_69f63c663be481908f233d25d28713a4 |
completed | May 2, 2026, 6:03 p.m. |
Created at: April 27, 2026, 2:43 p.m.